Displaying similar documents to “Non-split almost complex and non-split Riemannian supermanifolds”

High-order angles in almost-Riemannian geometry

Ugo Boscain, Mario Sigalotti (2006-2007)

Séminaire de théorie spectrale et géométrie

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Let X and Y be two smooth vector fields on a two-dimensional manifold M . If X and Y are everywhere linearly independent, then they define a Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become linearly dependent somewhere on M , then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally...

A new class of almost complex structures on tangent bundle of a Riemannian manifold

Amir Baghban, Esmaeil Abedi (2018)

Communications in Mathematics

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In this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced ( 0 , 2 ) -tensor on the tangent bundle using these structures and Liouville 1 -form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.

The Laplace-Beltrami operator in almost-Riemannian Geometry

Ugo Boscain, Camille Laurent (2013)

Annales de l’institut Fourier

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We study the Laplace-Beltrami operator of generalized Riemannian structures on orientable surfaces for which a local orthonormal frame is given by a pair of vector fields that can become collinear. Under the assumption that the structure is 2-step Lie bracket generating, we prove that the Laplace-Beltrami operator is essentially self-adjoint and has discrete spectrum. As a consequence, a quantum particle cannot cross the singular set (i.e., the set where the vector fields...

On natural metrics on tangent bundles of Riemannian manifolds

Mohamed Tahar Kadaoui Abbassi, Maâti Sarih (2005)

Archivum Mathematicum

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There is a class of metrics on the tangent bundle T M of a Riemannian manifold ( M , g ) (oriented , or non-oriented, respectively), which are ’naturally constructed’ from the base metric g [Kow-Sek1]. We call them “ g -natural metrics" on T M . To our knowledge, the geometric properties of these general metrics have not been studied yet. In this paper, generalizing a process of Musso-Tricerri (cf. [Mus-Tri]) of finding Riemannian metrics on T M from some quadratic forms on O M × ℝ m to find metrics (not necessary...

Isotropic almost complex structures and harmonic unit vector fields

Amir Baghban, Esmaeil Abedi (2018)

Archivum Mathematicum

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Isotropic almost complex structures J δ , σ define a class of Riemannian metrics g δ , σ on tangent bundles of Riemannian manifolds which are a generalization of the Sasaki metric. In this paper, some results will be obtained on the integrability of these almost complex structures and the notion of a harmonic unit vector field will be introduced with respect to the metrics g δ , 0 . Furthermore, the necessary and sufficient conditions for a unit vector field to be a harmonic unit vector field will be obtained. ...

Modular Classes of Q-Manifolds, Part II: Riemannian Structures & Odd Killing Vectors Fields

Andrew James Bruce (2020)

Archivum Mathematicum

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We define and make an initial study of (even) Riemannian supermanifolds equipped with a homological vector field that is also a Killing vector field. We refer to such supermanifolds as Riemannian Q-manifolds. We show that such Q-manifolds are unimodular, i.e., come equipped with a Q-invariant Berezin volume.

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...