ON THE GEOMETRY OF THE TANGENT BUNDLE WITH VERTICAL RESCALED METRIC

被引：5

作者：

Dida, H. M. ^{[1
]}

Hathout, F. ^{[1
]}

Azzouz, A. ^{[1
]}

机构：

[1] Univ Saida, Fac Sci, Dept Math, Saida 20000, Algeria

来源：

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS | 2019年 / 68卷 / 01期

关键词：

Tangent bundle; vertical rescaled metric; Einstein structure; curvature; NATURAL METRICS;

D O I：

10.31801/cfsuasmas.443735

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (M, g) be a n-dimensional smooth Riemannian manifold. In the present paper, we introduce a new class of natural metrics denoted by G(f) and called the vertical rescaled metric on the tangent bundle TM. We calculate its Levi-Civita connection and Riemannian curvature tensor. We study the geometry of (TM, G(f)) and several important results are obtained on curvature, Einstein structure, scalar and sectional curvatures.

引用

页码：222 / 235

页数：14

共 23 条

[1]

Abbassi M.T.K., 2004, Comment. Math. Univ. Carol, V45, P591

[2]

Abbassi MTK, 2005, ARCH MATH-BRNO, V41, P71

[3] On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds [J].

Abbassi, MTK ;

Sarih, M .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2005, 22 (01) :19-47

[4]

[Anonymous], 1962, J REINE ANGEW MATH

[5] STRUCTURE OF COMPLETE MANIFOLDS OF NONNEGATIVE CURVATURE [J].

CHEEGER, J ;

GROMOLL, D .

ANNALS OF MATHEMATICS, 1972, 96 (03) :413-443

[6]

Dida H.M., 2009, Int. J. Math. Anal., V3, P443

[7]

Garcia-Rio D, 2010, MATH ITS APPL, V8

[8]

Gezer A, 2013, INT ELECTRON J GEOM, V6, P19

[9]

Gudmundsson S., 2002, Tokyo J. Math., V25, P75, DOI 10.3836/tjm/1244208938

[10]

GUDMUNDSSON S, 2002, EXPOS MATH, V0020, P00001, DOI [10.1016/S0723-0869(02)80027-5, DOI 10.1016/S0723-0869(02)80027-5]

← 1 2 3 →