scholarly journals Sasaki metric on the tangent bundle of a Weyl manifold

2018 ◽  
Vol 103 (117) ◽  
pp. 25-32 ◽  
Author(s):  
Cornelia-Livia Bejan ◽  
İlhan Gül
Keyword(s):  
Tangent Bundle ◽  
Sasaki Metric ◽  
Weyl Manifold

Let (M, [g]) be a Weyl manifold of dimension m > 2. By using the Sasaki metric G induced by g, we construct a Weyl structure on TM. Then we prove that it is never Einstein-Weyl unless (M, g) is flat. The main theorem here extends to the Weyl context a result of Musso and Tricerri.

scholarly journals N-Legendre and N-slant curves in the unit tangent bundle of Minkowski surfaces

2017 ◽  
Vol 11 (01) ◽  
pp. 1850008 ◽  
Author(s):  
Murat Bekar ◽  
Fouzi Hathout ◽  
Yusuf Yayli
Keyword(s):  
Tangent Bundle ◽  
Inner Product ◽  
Normal Vector ◽  
Sasaki Metric ◽  
Reeb Vector ◽  
Nonzero Constant ◽  
Unit Tangent Bundle ◽  
Slant Curves

Let [Formula: see text] be a unit tangent bundle of Minkowski surface [Formula: see text] endowed with the pseudo-Riemannian induced Sasaki metric. In this present paper, we studied the N-Legendre and N-slant curves in which the inner product of its normal vector and Reeb vector is zero and nonzero constant, respectively, in [Formula: see text] and several important characterizations of these curves are given.

scholarly journals The super-Sasaki metric on the antitangent bundle

2020 ◽  
Vol 17 (08) ◽  
pp. 2050122
Author(s):  
Andrew James Bruce
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Symplectic Form ◽  
Riemannian Metric ◽  
Riemannian Structure ◽  
Sasaki Metric

We show how to lift a Riemannian metric and almost symplectic form on a manifold to a Riemannian structure on a canonically associated supermanifold known as the antitangent or shifted tangent bundle. We view this construction as a generalization of Sasaki’s construction of a Riemannian metric on the tangent bundle of a Riemannian manifold.

Geodesics on the unit tangent bundle

2003 ◽  
Vol 133 (6) ◽  
pp. 1209-1229 ◽  
Author(s):  
J. Berndt ◽  
E. Boeckx ◽  
P. T. Nagy ◽  
L. Vanhecke
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Tangent Bundle ◽  
Unit Vector ◽  
Sphere Bundle ◽  
Sasaki Metric ◽  
Tangent Sphere Bundle ◽  
Tangent Sphere ◽  
Unit Tangent Bundle ◽  
Unit Tangent Sphere Bundle

A geodesic γ on the unit tangent sphere bundle T1M of a Riemannian manifold (M, g), equipped with the Sasaki metric gS, can be considered as a curve x on M together with a unit vector field V along it. We study the curves x. In particular, we investigate for which manifolds (M, g) all these curves have constant first curvature κ1 or have vanishing curvature κi for some i = 1, 2 or 3.

scholarly journals Study Concerning Berger Type Deformed Sasaki Metric on the Tangent Bundle

2019 ◽  
Vol 15 (4) ◽  
pp. 435-447
Author(s):  
Murat Altunbas ◽  
◽  
Ramazan Simsek ◽  
Aydın Gezer ◽  
◽  
...  
Keyword(s):  
Tangent Bundle ◽  
Sasaki Metric

scholarly journals The Metrics G = agS + bgH + cgV on the Tangent Bundle of a Weyl Manifold

2021 ◽  
Author(s):  
Murat Altunbaş
Keyword(s):  
Tangent Bundle ◽  
Linear Combinations ◽  
Weyl Manifold ◽  
Constant Coefficients

Let (M, [g]) be a Weyl manifold and TM be its tangent bundle equipped with Riemannian g−natural metrics which are linear combinations of Sasaki, horizontal and vertical lifts of the base metric with constant coefficients. The aim of this paper is to construct a Weyl structure on TM and to show that TM cannot be Einstein-Weyl even if (M, g) is fiat.

scholarly journals On the geometry of the tangent bundle with gradient Sasaki metric

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Lakehal Belarbi ◽  
Hichem Elhendi
Keyword(s):  
Curvature Tensor ◽  
Tangent Bundle ◽  
Riemannian Curvature ◽  
Curvature Scalar ◽  
Sasaki Metric ◽  
Content Type ◽  
Civita Connection ◽  
Riemannian Curvature Tensor ◽  
Sectional Curvatures ◽  
Levi Civita Connection

PurposeLet (M, g) be a n-dimensional smooth Riemannian manifold. In the present paper, the authors introduce a new class of natural metrics denoted by gf and called gradient Sasaki metric on the tangent bundle TM. The authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of (TM, gf) and several important results are obtained on curvature, scalar and sectional curvatures.Design/methodology/approachIn this paper the authors introduce a new class of natural metrics called gradient Sasaki metric on tangent bundle.FindingsThe authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of (TM, gf) and several important results are obtained on curvature scalar and sectional curvatures.Originality/valueThe authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of (TM, gf) and several important results are obtained on curvature scalar and sectional curvatures.

scholarly journals Slant Curves in the Unit Tangent Bundles of Surfaces

ISRN Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Zhong Hua Hou ◽  
Lei Sun
Keyword(s):  
Vector Field ◽  
Tangent Bundle ◽  
Unit Vector ◽  
Sasaki Metric ◽  
Geometric Properties ◽  
Unit Vector Field ◽  
Unit Tangent Bundle ◽  
Tangent Bundles ◽  
Slant Curves

Let (M,g) be a surface and let (U(TM),G) be the unit tangent bundle of M endowed with the Sasaki metric. We know that any curve Γ(s) in U(TM) consist of a curve γ(s) in M and as unit vector field X(s) along γ(s). In this paper we study the geometric properties γ(s) and X(s) satisfying when Γ(s) is a slant geodesic.

scholarly journals Geometry of Mus-Sasaki metric

2018 ◽  
Vol 26 (2) ◽  
pp. 113-126
Author(s):  
Abderrahim Zagane ◽  
Mustapha Djaa
Keyword(s):  
Scalar Curvature ◽  
Sectional Curvature ◽  
Tangent Bundle ◽  
Sasaki Metric ◽  
Sasakian Metrics

AbstractIn this paper, we introduce the Mus-Sasaki metric on the tangent bundle T M as a new natural metric non-rigid on T M. First we investigate the geometry of the Mus-Sasakian metrics and we characterize the sectional curvature and the scalar curvature.

Golden Riemannian structures on the tangent bundle with g-natural metrics

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2543-2554
Author(s):  
E. Peyghan ◽  
F. Firuzi ◽  
U.C. De
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Riemannian Metric

Starting from the g-natural Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g), we construct a family of the Golden Riemannian structures ? on the tangent bundle (TM,G). Then we investigate the integrability of such Golden Riemannian structures on the tangent bundle TM and show that there is a direct correlation between the locally decomposable property of (TM,?,G) and the locally flatness of manifold (M,g).

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