NDLI: A note on isometric immersions

Content Provider	Scilit
Author	Baikoussis, C. Brickell, F.
Copyright Year	1982
Description	Let N be a complete connected Riemannian manifold with sectional curvatures bounded from below. Let M be a complete simply connected Riemannian manifold with sectional curvatures $K_{M}$(σ)≤ $−a^{2}$ (a ≥ 0) and with dimension < 2 dim N. Suppose that N is isometrically immersed in M and that its image lies in a closed ball of radius ρ. Then $sup(K_{N}$(σ) − $K_{M}$(σ)) ≥ $μ^{2}(aρ)/ρ^{2}$ where the function μ is defined by μ(x) = x coth x for x > 0, μ(0) = 1 and the supremum is taken over all sections tangent to N.
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C03496BF2C115FED171175D885D3CB03/S1446788700018280a.pdf/div-class-title-a-note-on-isometric-immersions-div.pdf
Ending Page	166
Page Count	5
Starting Page	162
ISSN	02636115
DOI	10.1017/s1446788700018280
Journal	Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
Issue Number	2
Volume Number	33
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	1982-10-01
Access Restriction	Open
Subject Keyword	Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics Applied Mathematics Isometric Immersions
Content Type	Text

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