The Euler characteristics and Weyl's curvature invariants of submanifolds in spheres

Toru ISHIHARA

doi:10.2969/jmsj/03920247

Toru ISHIHARA

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1987 年 39 巻 2 号 p. 247-256

DOI https://doi.org/10.2969/jmsj/03920247

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Published: 1987 Received: 1985/02/25 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) B. Y. Chen, On the total curvature of immersed manifolds, I: An inequality of Fenchel-Borsuk-Willmore, Amer. J. Math., 93 (1971), 148-162.
2) S. S. Chern, On the kinematic formula in integral geometry, J. Math. Mech., 16 (1966), 101-118.
3) B. Guillmein and A. Pollack, Differential Topology, Prentice-Hall, 1974.
4) A. Gray, Comparison theorems for the volumes of tubes as generalizations of the Weyl tube formula, Topology, 21 (1982), 201-228.
5) R. Langevin and T. Shifrin, Polar varieties and integral geometry, Amer. J. Math., 104 (1982), 553-605.
6) L. A. Santalo, Integral geometry and geometric probability, Encyclopedia of Mathematics and Its Applications, Addison-Wesley, 1976.
7) E. Teufel, Eine differentialtopologische Berechnung der Totalen Krümmung und Totalen Absolutkrümmung in der sphärischen Differentialgeometrie, Manuscripta Math., 31 (1980), 119-147.
8) E. Teufel, Anwendung der differentialtopologischen Berechnung der Totalen Krümmung und Totalen Absolutkrümmung in der sphärischen Differentialgeometrie, Manuscripta Math., 32 (1980), 239-262.
9) E. Teufel, Differential topology and the computation of total absolute curvature, Math. Ann., 258 (1982), 471-480.
10) H. Weyl, On the volume of tubes, Amer. J. Math., 61 (1939), 461-472.

Right : [1] B. Y. Chen, On the total curvature of immersed manifolds, I: An inequality of Fenchel-Borsuk-Willmore, Amer. J. Math., 93 (1971), 148-162.
[2] S. S. Chern, On the kinematic formula in integral geometry, J. Math. Mech., 16 (1966), 101-118.
[3] B. Guillmein and A. Pollack, Differential Topology, Prentice-Hall, 1974.
[4] A. Gray, Comparison theorems for the volumes of tubes as generalizations of the Weyl tube formula, Topology, 21 (1982), 201-228.
[5] R. Langevin and T. Shifrin, Polar varieties and integral geometry, Amer. J. Math., 104 (1982), 553-605.
[6] L. A. Santalo, Integral geometry and geometric probability, Encyclopedia of Mathematics and Its Applications, Addison-Wesley, 1976.
[7] E. Teufel, Eine differentialtopologische Berechnung der Totalen Krümmung und Totalen Absolutkrümmung in der sphärischen Differentialgeometrie, Manuscripta Math., 31 (1980), 119-147.
[8] E. Teufel, Anwendung der differentialtopologischen Berechnung der Totalen Krümmung und Totalen Absolutkrümmung in der sphärischen Differentialgeometrie, Manuscripta Math., 32 (1980), 239-262.
[9] E. Teufel, Differential topology and the computation of total absolute curvature, Math. Ann., 258 (1982), 471-480.
[10] H. Weyl, On the volume of tubes, Amer. J. Math., 61 (1939), 461-472.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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