松下 泰雄

Yasuo Matsushita
滋賀県立大学名誉教授
大阪市立大学数学研究所
大阪大学工学部非常勤講師
微分幾何学および微分トポロジー,理論物理学の背景となる数学,応用数学,工学における数学

著書

『機械工学系のための数学』

松下泰雄著,サイエンス社・数理工学社(2019年12月25日発行)
サイエンス社ホームページ

「正誤表」
微分を積分で定義する
 本書の第1章微積分において,不連続関数の微分が積分によって定義されること,そこにデルタ関数が登場することを説いた(シュワルツの「超関数論」の発端となるアイデア).デルタ関数は,標準的なカリキュラムにおいて,フーリエ解析やラプラス変換における必須の部品のように扱われ,しかも定義は簡単なイメージですまされていることが少なくないと感じてきた.デルタ関数によって不連続関数の微分が可能となるという微積分の観点からの教育は欠如していると思われる.微積分において導入されたデルタ関数を取り込むことによって,フーリエ変換やラプラス変換の威力が増すと説く.本書は,世にあふれている不連続関数の世界へ踏み込んでいくことのできる微積分の力を示して,機械工学を根幹とする工学における数学を展開する.

『曲線の秘密』

(B1961, ブルーバックス)
松下泰雄著,講談社(2016年3月20日発行)
講談社BOOK倶楽部
書評: 資料2-日経サイエンス 2016年6月号 新刊ガイド (pp.110-111) 紹介記事
現代ビジネス「読書人の雑誌『本』」 2016年4月5日より 紹介記事

『4次元微分幾何学への招待』

(不定計量の存在,ニュートラル計量,複素曲面,ツイスター )
松下泰雄・鎌田博行・中田文憲共著,臨時別冊・数理科学 SGCライブラリ-113, サイエンス社(2014年12月発行)
サイエンス社ホームページ

『波のしくみ』

(B1575, ブルーバックス)
佐藤文隆,松下泰雄共著,講談社(2007年11月発行)
講談社BOOK倶楽部
書評: 電子情報通信学会 通信ソサエティマガジン No.9 [夏号] 2009,[この本をお勧めします 若手の技術者と研究者へ]

講談社ブック倶楽部 電子書籍

『フーリエ解析 = 基礎と応用』

松下泰雄著,培風館(2001年10月発行)(2019年20刷)

解説・寄稿


論文リスト

  1. Matsushita, Yasuo
    Lecture note on indefinite manifolds and related topics
    (February 22, 23, 2018)
    Proceedings of the 21st International Workshop on Hermitian Symmetric Spaces and Submanifolds and
    14th RIRCM-OCAMI Joint Differential Geometry Workshop, 111 - 174,
    Kyungpook National Universit, Daegu, Korea 2017 (Issued in 2018).
    MR3793893
  2. Matsushita, Yasuo; Law, Peter R.
    Counterexamples to Goldberg conjecture with reversed orientation on Walker 8-manifolds of neutral signature.
    Hermitian-Grassmannian submanifolds, 101 - 114, Springer Proc. Math. Stat., 203, Springer, Singapore, 2017.
    MR3710836
    (Correction:   P.102 line 16:   $(r/2 \leq n)$ should read $(2r \leq n)$ )
  3. Kimura, Masayuki; Matsushita, Yasuo; Hikihara, Takashi
    Parametric resonance of intrinsic localized modes in coupled cantilever arrays.
    Phys. Lett. A 380 (2016), no. 36, 2823 - 2827. 70K28 (34A33)
    MR3531509
  4. Matsushita, Yasuo; Law, Peter R.; Katayama, Noriaki
    Neutral geometry in 4-dimension and counterexamples to Goldberg conjecture constructed on Walker 6-manifolds.
    Proceedings of the 19th International Workshop on Hermitian-Grassmannian Submanifolds and 10th RIRCM-
    OCAMI Joint Differential Geometry Workshop, 1 - 14, Natl. Inst. Math. Sci. (NIMS), Taejŏn, 2015.
    (There are some typos in (9.3). Here is the corrected paper.)
    MR3699631
  5. Law, Peter R.; Matsushita, Yasuo
    Real AlphaBeta-geometries and Walker geometry.
    J. Geom. Phys. 65 (2013), 35 - 44.
    MR3005772
  6. Matsushita, Yasuo
    Geometric structures in four-dimension and almost Hermitian structures.
    International Workshop on Complex Structures, Integrability and Vector Fields, 66 - 80, AIP Conf. Proc., 1340,
    Amer. Inst. Phys., Melville, NY, 2011.
    MR3051051
  7. Law, Peter R.; Matsushita, Yasuo
    Algebraically special, real alpha-geometries.
    J. Geom. Phys. 61 (2011), no. 11, 2064 - 2080.
    MR2827110
  8. García-Río, Eduardo; Haze, Seiya; Katayama, Noriaki; Matsushita, Yasuo
    Symplectic, Hermitian and Kahler structures on Walker 4-manifolds.
    J. Geom. 90 (2008), no. 1-2, 56 - 65.
    MR2465786
  9. Law, Peter R.; Matsushita, Yasuo
    A spinor approach to Walker geometry.
    Comm. Math. Phys. 282 (2008), no. 3, 577 - 623.
    MR2426138
  10. Davidov, J.; Díaz-Ramos, J. C.; García-Río, E.; Matsushita, Y.; Muškarov, O.;
    Vazquez-Lorenzo, R.

    Hermitian-Walker 4-manifolds.
    J. Geom. Phys. 58 (2008), no. 3, 307 - 323.
    MR2394040
  11. Matsushita, Y.
    Counterexamples of compact type to the Goldberg conjecture and various version of the conjecture.
    Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics, 222 - 233,
    World Sci. Publ., Hackensack, NJ, 2007.
    MR2362613
  12. Matsushita, Yasuo; Haze, Seiya; Law, Peter R.
    Almost Kahler-Einstein structures on 8-dimensional Walker manifolds.
    Monatsh. Math. 150 (2007), no. 1, 41 - 48.
    MR2297252
  13. Davidov, J.; Díaz-Ramos, J. C.; García-Río, E.; Matsushita, Y.; Muškarov, O.;
    Vazquez-Lorenzo, R.

    Almost Kähler Walker 4-manifolds.
    J. Geom. Phys. 57 (2007), no. 3, 1075 - 1088.
    MR2275210
  14. Matsushita, Yasuo
    Four-dimensional geometric structures and almost complex structures? solvmanifolds Sol4m,n (neutral version).
    III-N.
    JP J. Geom. Topol. 6 (2006), no. 2, 197 - 210.
    MR2273595
  15. Matsushita, Yasuo
    Four-dimensional geometric structures and almost complex structures? nilmanifolds Nil4 (neutral version). II-N.
    JP J. Geom. Topol. 6 (2006), no. 2, 183 - 195.
    MR2273594
  16. Matsushita, Yasuo
    Four-dimensional geometric structures and almost complex structures? product manifolds H3×E1
    (Riemannian version). IV-R.
    JP J. Geom. Topol. 6 (2006), no. 1, 35 - 44.
    MR2237629
  17. Matsushita, Yasuo
    Four-dimensional geometric structures and almost complex structures: solvmanifolds Sol4m,n
    (Riemannian version). III-R.
    JP J. Geom. Topol. 6 (2006), no. 1, 25 - 33.
    MR2237628
  18. Matsushita, Yasuo
    Four-dimensional manifolds with two kinds of double almost Hermitian structures.
    JP J. Geom. Topol. 6 (2006), no. 1, 1 - 23.
    MR2237627
  19. Matsushita, Yasuo
    Four-dimensional geometric structures and almost complex structures. Ggeneral Procedure (neutral version).
    I-N.
    JP J. Geom. Topol. 5 (2005), no. 3, 251 - 274.
    MR2184806
  20. Matsushita, Yasuo
    Professor Kouei Sekigawa and his friends in mathematics.
    Topics in Almost Hermitian Geometry and Related Fields, 257 - 263, World Sci. Publ., Hackensack, NJ, 2005.
    01A70
    MR2181508
  21. García-Ramírez, Iago; García-Río, Eduardo; Matsushita, Yasuo
    Application of Bochner-Weizenbock formulas to symplectic and complex pairs to be Kahler pairs in dimension
    four,
    Topics in Almost Hermitian Geometry and Related Fields, 74 - 86, World Sci. Publ., Hackensack, NJ, 2005.
    MR2181493
  22. Matsushita, Yasuo
    Four-dimensional geometric structures and almost complex structures?nilmanifolds Nil4 (Riemannian version).
    II-R.
    JP J. Geom. Topol. 5 (2005), no. 2, 177 - 186.
    MR2180592
  23. Matsushita, Yasuo
    Four-dimensional geometric structures and almost complex structures?general procedure (Riemannian version).
    I-R.
    JP J. Geom. Topol. 5 (2005), no. 2, 155 - 176.
    MR2180591
  24. Bonome, A.; Castro, R.; Hervella, L. M.; Matsushita, Y.
    Flat almost Norden metrics with nonintegrable almost complex structures in dimension four.
    JP J. Geom. Topol. 5 (2005), no. 2, 141 - 153.
    MR2180590
  25. Bonome, A.; Castro, R.; Hervella, L. M.; Matsushita, Y.
    Construction of Norden structures on neutral 4-manifolds.
    JP J. Geom. Topol. 5 (2005), no. 2, 121 - 140.
    MR2180589
  26. Matsushita, Yasuo
    On Euler characteristics and Hirzebruch indices of four-dimensional almost para-Hermitian manifolds.
    JP J. Geom. Topol. 5 (2005), no. 2, 115 - 120.
    MR2180588
  27. Matsushita, Yasuo
    The existence of indefinite metrics of signature $(+ + - -)$ and two kinds of almost complex structures in dimension
    four.
    Contemporary Aspects of Complex Analysis, Differential Geometry and Mathematical Physics, 210 - 226, World
    Sci. Publ., Hackensack, NJ, 2005.
    MR2180565
  28. Matsushita, Yasuo
    Walker 4-manifolds with proper almost complex structures.
    J. Geom. Phys. 55 (2005), no. 4, 385 - 398.
    MR2162417
  29. Chaichi, M.; García-Río, E.; Matsushita, Y.
    Curvature properties of four-dimensional Walker metrics.
    Classical Quantum Gravity 22 (2005), no. 3, 559 - 577.
    MR2115361
  30. Matsushita, Yasuo
    Four-dimensional Walker metrics and symplectic structures.
    J. Geom. Phys. 52 (2004), no. 1, 89 - 99.
    MR2085665
  31. Matsushita, Yasuo; Law, Peter
    Hitchin-Thorpe-type inequalities for pseudo-Riemannian 4-manifolds of metric signature $(+ + - -)$.
    Geom. Dedicata 87 (2001), no. 1-3, 65 - 89.
    MR1866843
  32. García-Río, Eduardo; Matsushita, Yasuo; Vazquez-Lorenzo, Ramon
    Paraquaternionic Kahler manifolds.
    Rocky Mountain J. Math. 31 (2001), no. 1, 237 - 260.
    MR1821379
  33. García-Río, Eduardo; Matsushita, Yasuo
    Isotropic Kahler structures on Engel 4-manifolds.
    J. Geom. Phys. 33 (2000), no. 3-4, 288 - 294.
    MR1747036
  34. Bonome, A.; Castro, R.; García-Río, E.; Hervella, L. M.; Matsushita, Y.
    Pseudo-Chern classes and opposite Chern classes of indefinite almost Hermitian manifolds.
    Acta Math. Hungar. 75 (1997), no. 4, 299 - 316.
    MR1448706
  35. Matsushita, Yasuo
    Equivalence classes of fields of 2-planes and two kinds of almost complex structures on compact four-dimensional
    manifolds.
    Manuscripta Math. 88 (1995), no. 4, 409 - 415.
    MR1362927
  36. Bonome, A.; Castro, R.; García-Río, E.; Hervella, L.; Matsushita, Y.
    The Kahler-Einstein metrics on a K3 surface cannot be almost Kahler with respect to an opposite almost complex structure.
    Kodai Math. J. 18 (1995), no. 3, 506 - 514.
    MR1362925
  37. Bonome, A.; Castro, R.; García-Río, E.; Hervella, L. M.; Matsushita, Y.
    Null holomorphically flat indefinite almost Hermitian manifolds.
    Illinois J. Math. 39 (1995), no. 4, 635 - 660.
    MR1361526
  38. Bonome, A.; Castro, R.; García-Río, E.; Hervella, L. M.; Matsushita, Y.
    Almost complex manifolds with holomorphic distributions.
    Rend. Mat. Appl. (7) 14 (1994), no. 4, 567 - 589.
    MR1312818
  39. Matsushita, Yasuo
    Some remarks on fields of 2-planes on compact smooth 4-manifolds.
    Progress in differential geometry, 153 - 167, Adv. Stud. Pure Math., 22, Math. Soc. Japan, 1993.
    MR1274946
  40. Matsushita, Yasuo
    Fields of 2-planes and two kinds of almost complex structures on compact 4-dimensional manifolds.
    Math. Z. 207 (1991), no. 2, 281 - 291.
    MR1109666
  41. Matsushita, Yasuo
    Fields of 2-planes on compact simply-connected smooth 4-manifolds.
    Math. Ann. 280 (1988), no. 4, 687 - 689.
    MR0939927
  42. Matsushita, Yasuo
    Pseudo-Chern classes of an almost pseudo-Hermitian manifold.
    Trans. Amer. Math. Soc. 301 (1987), no. 2, 665 - 677.
    MR0882709
  43. Katayama, Noriaki; Matsushita, Yasuo
    A problem on closed orbits in a cosmological model.
    Tensor (N.S.) 42 (1985), no. 2, 173 - 178.
    MR0838529
  44. Matsushita, Yasuo
    Pseudo-Pontrjagin classes.
    Proc. Amer. Math. Soc. 93 (1985), no. 3, 521 - 524.
    MR0774016
  45. Matsushita, Yasuo
    Thorpe-Hitchin inequality for compact Einstein 4-manifolds of metric signature $(+ + - -)$ and the generalized
    Hirzebruch index formula.
    J. Math. Phys. 24 (1983), no. 1, 36 - 40.
    MR0690367
  46. Matsushita, Yasuo
    Inequality for the Euler characteristic of compact Einstein 4-manifolds.
    Math. Japon. 26 (1981), no. 1, 77 - 79.
    MR0613469
  47. Matsushita, Yasuo
    On Euler characteristics of compact Einstein 4-manifolds of metric signature $(+ + - -)$.
    J. Math. Phys. 22 (1981), no. 5, 979 - 982.
    MR0622847

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