Pseudo-Riemannian weakly symmetric manifolds of low dimension

Bo Zhang; Zhiqi Chen; Shaoqiang Deng

Displaying similar documents to “Pseudo-Riemannian weakly symmetric manifolds of low dimension”

An explicit classification of 3-dimensional Riemannian spaces satisfying $R (X, Y) \cdot R = 0$

Oldřich Kowalski (1996)

Czechoslovak Mathematical Journal

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Fredholmness of pseudo-differential operators with nonregular symbols

Kazushi Yoshitomi (2023)

Czechoslovak Mathematical Journal

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We establish the Fredholmness of a pseudo-differential operator whose symbol is of class $C^{0, σ}$ , $0 < σ < 1$ , in the spatial variable. Our work here refines the work of H. Abels, C. Pfeuffer (2020).

Riemannian semisymmetric almost Kenmotsu manifolds and nullity distributions

Yaning Wang, Ximin Liu (2014)

Annales Polonici Mathematici

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We consider an almost Kenmotsu manifold $M^{2 n + 1}$ with the characteristic vector field ξ belonging to the (k,μ)’-nullity distribution and h’ ≠ 0 and we prove that $M^{2 n + 1}$ is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant sectional curvature -4 and a flat n-dimensional manifold, provided that $M^{2 n + 1}$ is ξ-Riemannian-semisymmetric. Moreover, if $M^{2 n + 1}$ is a ξ-Riemannian-semisymmetric almost Kenmotsu manifold such that ξ belongs to the (k,μ)-nullity distribution, we prove...

Killing spinor-valued forms and the cone construction

Petr Somberg, Petr Zima (2016)

Archivum Mathematicum

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On a pseudo-Riemannian manifold $𝕄$ we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of Killing equations on $𝕄$ and parallel fields on the metric cone over $𝕄$ for spinor-valued forms.

Collapse of warped submersions

Szymon M. Walczak (2006)

Annales Polonici Mathematici

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We generalize the concept of warped manifold to Riemannian submersions π: M → B between two compact Riemannian manifolds $(M, g_{M})$ and $(B, g_{B})$ in the following way. If f: B → (0,∞) is a smooth function on B which is extended to a function f̂ = f ∘ π constant along the fibres of π then we define a new metric $g_{f}$ on M by $g_{f} |_{\times} \equiv g_{M} |_{\times}, g_{f} {|_{\times T M ̂} \equiv f ̂ ² g_{M} |}_{\times T M ̂}$ , where and denote the bundles of horizontal and vertical vectors. The manifold $(M, g_{f})$ obtained that way is called a warped submersion. The function f is called a warping function. We show...

Continuous pseudo-hairy spaces and continuous pseudo-fans

Janusz R. Prajs (2002)

Fundamenta Mathematicae

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A compact metric space X̃ is said to be a continuous pseudo-hairy space over a compact space X ⊂ X̃ provided there exists an open, monotone retraction $r : X ̃ \binom{o n t o}{⟶} X$ such that all fibers $r^{- 1} (x)$ are pseudo-arcs and any continuum in X̃ joining two different fibers of r intersects X. A continuum $Y_{X}$ is called a continuous pseudo-fan of a compactum X if there are a point $c \in Y_{X}$ and a family ℱ of pseudo-arcs such that $⋃ ℱ = Y_{X}$ , any subcontinuum of $Y_{X}$ intersecting two different elements of ℱ contains c, and ℱ is homeomorphic...

Tenseness of Riemannian flows

Hiraku Nozawa, José Ignacio Royo Prieto (2014)

Annales de l’institut Fourier

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We show that any transversally complete Riemannian foliation $ℱ$ of dimension one on any possibly non-compact manifold $M$ is tense; namely, $M$ admits a Riemannian metric such that the mean curvature form of $ℱ$ is basic. This is a partial generalization of a result of Domínguez, which says that any Riemannian foliation on any compact manifold is tense. Our proof is based on some results of Molino and Sergiescu, and it is simpler than the original proof by Domínguez. As an application, we generalize...

Global existence of solutions to Schrödinger equations on compact riemannian manifolds below $H^{1}$

Sijia Zhong (2010)

Bulletin de la Société Mathématique de France

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In this paper, we will study global well-posedness for the cubic defocusing nonlinear Schrödinger equations on the compact Riemannian manifold without boundary, below the energy space, i.e. $s < 1$ , under some bilinear Strichartz assumption. We will find some $\tilde{s} < 1$ , such that the solution is global for $s > \tilde{s}$ .

On $G$ -sets and isospectrality

Ori Parzanchevski (2013)

Annales de l’institut Fourier

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We study finite $G$ -sets and their tensor product with Riemannian manifolds, and obtain results on isospectral quotients and covers. In particular, we show the following: If $M$ is a compact connected Riemannian manifold (or orbifold) whose fundamental group has a finite non-cyclic quotient, then $M$ has isospectral non-isometric covers.

On a question of Demailly-Peternell-Schneider

Meng Chen, Qi Zhang (2013)

Journal of the European Mathematical Society

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We give an affirmative answer to an open question posed by Demailly-Peternell-Schneider in 2001 and recently by Peternell. Let $f : X \to Y$ be a surjective morphism from a log canonical pair $(X, D)$ onto a $ℚ$ -Gorenstein variety $Y$ . If $- (K_{X} + D)$ is nef, we show that $- K_{Y}$ is pseudo-effective.

Some Classes of Lorentzian $α$ -Sasakian Manifolds Admitting a Quarter-symmetric Metric Connection

Santu DEY, Buddhadev Pal, Arindam BHATTACHARYYA (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The object of the present paper is to study a quarter-symmetric metric connection in an Lorentzian $α$ -Sasakian manifold. We study some curvature properties of an Lorentzian $α$ -Sasakian manifold with respect to the quarter-symmetric metric connection. We study locally $φ$ -symmetric, $φ$ -symmetric, locally projective $φ$ -symmetric, $ξ$ -projectively flat Lorentzian $α$ -Sasakian manifold with respect to the quarter-symmetric metric connection.

Pseudo-boundaries and pseudo-interiors for topological convexities

M. Van de Vel

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CONTENTS0. Introduction......... .............................................................51. Topological convexity structures.......................................62. Half-spaces and related results......................................123. Pseudo-boundaries........................................................254. The Krein-Milman theorem.............................................335. Pseudo-interiority...........................................................406. The existence...