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Bull. Korean Math. Soc. 2017; 54(1): 253-264

Online first article January 12, 2017      Printed January 31, 2017

https://doi.org/10.4134/BKMS.b160082

Copyright © The Korean Mathematical Society.

Circles along a Riemannian map and Clairaut Riemannian maps

Bayram \c{S}ahin

Ege University

Abstract

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We first extend Yano-Nomizu's theorem, which characterizes extrinsic spheres in a Riemannian manifold, for Riemannian maps. Then we introduce Clairaut Riemannian maps, give an example and obtain necessary and sufficient conditions for a Riemannian map to be Clairaut type.

Keywords: Riemannian map, circle, Clairaut submersion, Clairaut Riemannian map

MSC numbers: 53C42, 53C20

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