Bayram Şahin
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.
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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.
Key concepts: Exponential map (Riemannian geometry), Mathematics, Fundamental theorem of Riemannian geometry, Riemannian manifold, Riemannian geometry, Riemannian submersion, Manifold (fluid mechanics), Mathematical analysis