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An Integral Formula and Inverse Fundamental Forms on Hypersurfaces In Riemannian Manifolds

Year 1983, Volume: 32 , - , 01.01.1983
https://doi.org/10.1501/Commua1_0000000234

Abstract

In this study, the coefficients of the p-fundamental forms of a hypersurface N imbedded in n-dimensional Riemannian space M were expressed in terms of the coefficients of first and se- cond fundamental forms. Then, by means of Cayley-Hamilton theorem, the inverse S-1 of the shape operatör S on the hypersurface N was vvritten as the combinations of the powers of S and the curvatures K n ... K p Thus the new fundamental forms and some properties of them cal- led the inverse fundamental forms, were defined and investigated. As a result of an application of the generalized divergence theorem of Gauss to the divergence relations of certain tensor fi- elds över the region R of N that can be expressed in terms of polynomials involving the new de­ fined curvatures of M an integral formula was obtained.

References

  • Communications, Series A1:Mathematics and Statistics
Year 1983, Volume: 32 , - , 01.01.1983
https://doi.org/10.1501/Commua1_0000000234

Abstract

References

  • Communications, Series A1:Mathematics and Statistics
There are 1 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

M. Erdoğan This is me

Publication Date January 1, 1983
Submission Date January 1, 1983
Published in Issue Year 1983 Volume: 32

Cite

APA Erdoğan, M. (1983). An Integral Formula and Inverse Fundamental Forms on Hypersurfaces In Riemannian Manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 32. https://doi.org/10.1501/Commua1_0000000234
AMA Erdoğan M. An Integral Formula and Inverse Fundamental Forms on Hypersurfaces In Riemannian Manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. January 1983;32. doi:10.1501/Commua1_0000000234
Chicago Erdoğan, M. “An Integral Formula and Inverse Fundamental Forms on Hypersurfaces In Riemannian Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 32, January (January 1983). https://doi.org/10.1501/Commua1_0000000234.
EndNote Erdoğan M (January 1, 1983) An Integral Formula and Inverse Fundamental Forms on Hypersurfaces In Riemannian Manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 32
IEEE M. Erdoğan, “An Integral Formula and Inverse Fundamental Forms on Hypersurfaces In Riemannian Manifolds”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 32, 1983, doi: 10.1501/Commua1_0000000234.
ISNAD Erdoğan, M. “An Integral Formula and Inverse Fundamental Forms on Hypersurfaces In Riemannian Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 32 (January 1983). https://doi.org/10.1501/Commua1_0000000234.
JAMA Erdoğan M. An Integral Formula and Inverse Fundamental Forms on Hypersurfaces In Riemannian Manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 1983;32. doi:10.1501/Commua1_0000000234.
MLA Erdoğan, M. “An Integral Formula and Inverse Fundamental Forms on Hypersurfaces In Riemannian Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 32, 1983, doi:10.1501/Commua1_0000000234.
Vancouver Erdoğan M. An Integral Formula and Inverse Fundamental Forms on Hypersurfaces In Riemannian Manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 1983;32.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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