Curvature of a Submanifold in Rn
Abstract
The curvature of a Euclidean submanifold is perhaps one of the most basic questions in Riemannian Geometry, although it is somehow not generally discussed in a lot of textbooks. So we give a survey of and an answer to this basic question in this article. More importantly
we provide a new method of answering this question, which, compared to the old method, is simpler computationally and clearer theoretically.
we provide a new method of answering this question, which, compared to the old method, is simpler computationally and clearer theoretically.
Keywords
Curvature; Second fundamental form; Transposition map; m-fold; Vector fields
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[1] Manfredo Perdigo do Carmo, Translated by Francis Flaherty, Remannian Geometry, Birkhuser Boston, 1982.
[2] Kobayashi Shoshichi, Nomizu Katsumi, Foundations of Differential Geometry, Vol. 1 (New ed.), Wiley-Interscience, 1996.
[3] Peter Petersen, Riemannian Geometry, Berlin: Springer-Verlag, 2006.
[4] Jeff Cheeger, David G. Ebin, Comparison theorems in Riemannian geometry, Providence, RI: AMS Chelsea Publishing, 2008.
[5] Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine, Riemannian geometry, Universitext (3rd ed.), Berlin: Springer-Verlag, 2004.
[6] Jrgen Jost, Riemannian Geometry and Geometric Analysis, Berlin: Springer-Verlag, 2022.
DOI: http://dx.doi.org/10.70711/frim.v3i12.7907
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