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2015•Annals of the Alexandru Ioan Cuza University - MathematicsOpen access

A Survey on Differential Geometry of Riemannian Maps Between

Bayram Şahin

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Abstract

Abstract The main aim of this paper is to state recent results in Riemannian geometry obtained by the existence of a Riemannian map between Riemannian manifolds and to introduce certain geometric objects along such maps which allow one to use the techniques of submanifolds or Riemannian submersions for Riemannian maps. The paper also contains several open problems related to the research area.

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What this paper is about

Abstract The main aim of this paper is to state recent results in Riemannian geometry obtained by the existence of a Riemannian map between Riemannian manifolds and to introduce certain geometric objects along such maps which allow one to use the techniques of submanifolds or Riemannian submersions for Riemannian maps. The paper also contains several open problems related to the research area.

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Available abstract

Abstract The main aim of this paper is to state recent results in Riemannian geometry obtained by the existence of a Riemannian map between Riemannian manifolds and to introduce certain geometric objects along such maps which allow one to use the techniques of submanifolds or Riemannian submersions for Riemannian maps. The paper also contains several open problems related to the research area.

Key concepts: Riemannian geometry, Curvature of Riemannian manifolds, Fundamental theorem of Riemannian geometry, Differential geometry, Mathematics, Exponential map (Riemannian geometry), Information geometry, Geometric analysis

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