On anti-invariant Riemannian submersions whose total manifolds are locally product Riemannian

Hakan Mete Taṣtan; Fatma Özdemir; Cem Sayar

doi:10.1007/s00022-016-0347-x

On anti-invariant Riemannian submersions whose total manifolds are locally product Riemannian

Hakan Mete Taṣtan, Fatma Özdemir, Cem Sayar^*

^*Corresponding author for this work

Department of Mathematics Engineering

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

In this paper, we study Riemannian, anti-invariant and Lagrangian submersions from locally product Riemannian manifolds onto Riemannian manifolds. We first give a characterization theorem for Riemannian submersions. It is proved that the fibers of a Lagrangian submersion are always totally geodesic. We also consider the first variational formula of anti-invariant Riemannian submersions and give a new condition for the harmonicity of such submersions.

Original language	English
Pages (from-to)	411-422
Number of pages	12
Journal	Journal of Geometry
Volume	108
Issue number	2
DOIs	https://doi.org/10.1007/s00022-016-0347-x
Publication status	Published - 1 Jul 2017

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing.

Keywords

anti-invariant submersions
first variational formula
horizontal distribution
Lagrangian submersion
locally product Riemannian manifold
Riemannian submersion

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10.1007/s00022-016-0347-x

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abstract = "In this paper, we study Riemannian, anti-invariant and Lagrangian submersions from locally product Riemannian manifolds onto Riemannian manifolds. We first give a characterization theorem for Riemannian submersions. It is proved that the fibers of a Lagrangian submersion are always totally geodesic. We also consider the first variational formula of anti-invariant Riemannian submersions and give a new condition for the harmonicity of such submersions.",

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AU - Özdemir, Fatma

AU - Sayar, Cem

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Y1 - 2017/7/1

N2 - In this paper, we study Riemannian, anti-invariant and Lagrangian submersions from locally product Riemannian manifolds onto Riemannian manifolds. We first give a characterization theorem for Riemannian submersions. It is proved that the fibers of a Lagrangian submersion are always totally geodesic. We also consider the first variational formula of anti-invariant Riemannian submersions and give a new condition for the harmonicity of such submersions.

AB - In this paper, we study Riemannian, anti-invariant and Lagrangian submersions from locally product Riemannian manifolds onto Riemannian manifolds. We first give a characterization theorem for Riemannian submersions. It is proved that the fibers of a Lagrangian submersion are always totally geodesic. We also consider the first variational formula of anti-invariant Riemannian submersions and give a new condition for the harmonicity of such submersions.

KW - anti-invariant submersions

KW - first variational formula

KW - horizontal distribution

KW - Lagrangian submersion

KW - locally product Riemannian manifold

KW - Riemannian submersion

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DO - 10.1007/s00022-016-0347-x

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EP - 422

JO - Journal of Geometry

JF - Journal of Geometry

IS - 2

ER -

On anti-invariant Riemannian submersions whose total manifolds are locally product Riemannian

Abstract

Bibliographical note

Keywords

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