Riemannian Submersions and Related Topics

Falcitelli, Maria; Pastore, Anna Maria; Ianuş, Stere

doi:10.1142/5568

Cited by 162 publications

(228 citation statements)

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“…For details on Riemannian submersions, we refer to O'Neill's paper [6] and to [2]. Finally, we recall that the notion of the second fundamental form of a map between Riemannian manifolds.…”

Section: Hemi-slant Submersionsmentioning

confidence: 99%

“…The fiber is called minimal, if H = 0, identically [2]. We now give a characterization theorem for the proper hemi-slant submersion with totally umbilical fibers.…”

Section: Hemi-slant Submersions With Totally Umbilical Fibersmentioning

confidence: 99%

“…Afterwards, almost Hermitian submersions have been actively studied between different subclasses of almost Hermitian manifolds, for example; see [3]. Most of the studies related to Riemannian or almost Hermitian submersions can be found in [2]. The study of antiinvariant Riemannian submersions from almost Hermitian manifolds were initiated by S .…”

Section: Introductionmentioning

confidence: 99%

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Hemi-Slant Submersions

2015

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As a generalization of anti-invariant submersions, semiinvariant submersions and slant submersions, we introduce the notion of hemi-slant submersion and study such submersions from Kählerian manifolds onto Riemannian manifolds. After we study the geometry of leaves of distributions which are involved in the definition of the submersion, we obtain new conditions for such submersions to be harmonic and totally geodesic. Moreover, we give a characterization theorem for the proper hemi-slant submersions with totally umbilical fibers.Mathematics Subject Classification. Primary 53C15, 53C43, 53B20.

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“…For details on Riemannian submersions, we refer to O'Neill's paper [6] and to [2]. Finally, we recall that the notion of the second fundamental form of a map between Riemannian manifolds.…”

Section: Hemi-slant Submersionsmentioning

confidence: 99%

“…The fiber is called minimal, if H = 0, identically [2]. We now give a characterization theorem for the proper hemi-slant submersion with totally umbilical fibers.…”

Section: Hemi-slant Submersions With Totally Umbilical Fibersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hemi-Slant Submersions

2015

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“…(a) If the fibers of π : M → B are totally geodesic, the flow Φ X H t described in the proof of Lemma 1.4 is an isometry of the fibers (e.g. [FPI,Cor. 2.1]).…”

Section: Fiber-harmonic Formsmentioning

confidence: 99%

A Hodge-Type Theorem for Manifolds with Fibered Cusp Metrics

Müller

2011

Geom. Funct. Anal.

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A manifold with fibered cusp metrics X can be considered as a geometrical generalization of locally symmetric spaces of Q-rank one at infinity. We prove a Hodge-type theorem for this class of Riemannian manifolds, i.e. we find harmonic representatives of the de Rham cohomology H p (X). Similar to the situation of locally symmetric spaces, these representatives are computed by special values or residues of generalized eigenforms of the Hodge-Laplace operator on Ω p (X).

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“…The Riemannian submersion was introduced by O'Neill in [6]. Since then, it has been effective tool to describe the structure of a Riemannian manifold (for more information about Riemannian submersions, see [3] and [8]). Note that the vertical distribution V of M is defined by V p = ker dφ p , p ∈ M. The orthogonal complementary distribution to V = ker dφ is defined by H p = (ker dφ p ) ⊥ , denoted by H and called horizontal.…”

Section: Introductionmentioning

confidence: 99%

On a Submersion Between Reinhart Lightlike Manifolds and Semi-Riemannian Manifolds

Şahin

2008

MedJM

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In this paper, we introduce a new submersion, namely, screen lightlike submersion between a lightlike manifold and a semi-Riemannian manifold. We give an example and obtain a characterization for lightlike manifold to be Reinhart under such submersion. Then, we investigate the geometry of a screen lightlike submersion when the total manifold is a Reinhart lightlike manifold. Mathematics Subject Classification (2000). Primary 53C20; Secondary 53C50.

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Riemannian Submersions and Related Topics

Cited by 162 publications

References 0 publications

Hemi-Slant Submersions

Hemi-Slant Submersions

A Hodge-Type Theorem for Manifolds with Fibered Cusp Metrics

On a Submersion Between Reinhart Lightlike Manifolds and Semi-Riemannian Manifolds

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