Tokyo Journal of Mathematics

Theorems of Gauss-Bonnet and Chern-Lashof Types in a Simply Connected Symmetric Space of Non-Positive Curvature

Naoyuki KOIKE

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Abstract

In this paper, we shall generalize the Gauss-Bonnet and Chern-Lashof theorems to compact submanifolds in a simply connected symmetric space of non-positive curvature. Those proofs are performed by applying the Morse theory to squared distance functions because height functions are not defined.

Article information

Source
Tokyo J. Math., Volume 26, Number 2 (2003), 527-539.

Dates
First available in Project Euclid: 5 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1244208606

Digital Object Identifier
doi:10.3836/tjm/1244208606

Mathematical Reviews number (MathSciNet)
MR2020801

Zentralblatt MATH identifier
1048.53041

Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 53C40: Global submanifolds [See also 53B25]

Citation

KOIKE, Naoyuki. Theorems of Gauss-Bonnet and Chern-Lashof Types in a Simply Connected Symmetric Space of Non-Positive Curvature. Tokyo J. Math. 26 (2003), no. 2, 527--539. doi:10.3836/tjm/1244208606. https://projecteuclid.org/euclid.tjm/1244208606


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