2017
Том 69
№ 9

All Issues

On an invariant on isometric immersions into spaces of constant sectional curvature

Rivertz H. J.

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Abstract

In the present paper, we give an invariant on isometric immersions into spaces of constant sectional curvature. This invariant is a direct consequence of the Gauss equation and the Codazzi equation of isometric immersions. We apply this invariant on some examples. Further, we apply it to codimension 1 local isometric immersions of 2-step nilpotent Lie groups with arbitrary leftinvariant Riemannian metric into spaces of constant nonpositive sectional curvature. We also consider the more general class, namely, three-dimensional Lie groups $G$ with nontrivial center and with arbitrary left-invariant metric. We show that if the metric of $G$ is not symmetric, then there are no local isometric immersions of $G$ into $Q_{c^4}$.

English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 12, pp 1946-1955.

Citation Example: Rivertz H. J. On an invariant on isometric immersions into spaces of constant sectional curvature // Ukr. Mat. Zh. - 2009. - 61, № 12. - pp. 1660-1704.

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