J. C. Gonzalez-Davila, M. C. Gonzalez-Davila, Departamento de Matematica Fundamental, Seccion de Geometria y Topologia, Universidad de La Laguna, La Laguna, Spain; L. Vanhecke, Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Leuven, Belgium
Abstract: We introduce the notions of (extrinsic) locally transversally symmetric immersions and submanifolds in a Riemannian manifold equipped with a unit Killing vector field as analogues of those of (extrinsic) locally symmetric immersions and submanifolds. We treat their geometric properties, derive several characterizations and give a list of examples.
Keywords: reflections, isometric flows, (locally) symmetric and transversally symmetric immersions and submanifolds, Killing-transversally symmetric spaces, normal flow space forms
Classification (MSC2000): 53B25, 53C25, 53C30, 53C40
Full text of the article: