Isotropic and Kähler Immersions

1 January 1965

journal article
Published by Canadian Mathematical Society in Canadian Journal of Mathematics

Vol. 17, 907-915
https://doi.org/10.4153/cjm-1965-086-7

Abstract

Let M^d and be Riemannian manifolds. We shall say that an isometric immersion ϕ: M^d —> is isotropic provided that all its normal curvature vectors have the same length. The class of such immersions is closed under compositions and Cartesian products. Umbilic immersions (e.g. S^d ⊂ R^d+1) are isotropic, but the converse does not hold. If M and are Kähler manifolds of constant holomorphic curvature, then any Kähler immersion of M in is automatically isotropic (Lemma 6). We shall find the smallest co-dimension for which there exist non-trivial immersions of this type, and obtain similar results in the real constant-curvature case.

Keywords

This publication has 1 reference indexed in Scilit:

Umbilics of constant curvature immersions
Duke Mathematical Journal, 1965