Tokyo Journal of Mathematics

The Gauss-Bonnet and Chern-Lashof Theorems in a Simply Connected Symmetric Space of Compact Type

Naoyuki KOIKE

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Abstract

In this paper, we prove the theorems of the Gauss-Bonnet and Chern-Lashof types for low dimensional compact submanifolds in a simply connected symmetric space of compact type. In particular, in the case where the ambient space is a sphere, we need not to give the restriction for the dimension of the submanifold. Those proofs are performed by applying the Morse theory to squared distance functions.

Article information

Source
Tokyo J. Math., Volume 28, Number 2 (2005), 483-497.

Dates
First available in Project Euclid: 5 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1244208203

Digital Object Identifier
doi:10.3836/tjm/1244208203

Mathematical Reviews number (MathSciNet)
MR2191062

Zentralblatt MATH identifier
1100.53057

Citation

KOIKE, Naoyuki. The Gauss-Bonnet and Chern-Lashof Theorems in a Simply Connected Symmetric Space of Compact Type. Tokyo J. Math. 28 (2005), no. 2, 483--497. doi:10.3836/tjm/1244208203. https://projecteuclid.org/euclid.tjm/1244208203


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References

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