scholarly journals THE CURVATURE OF HALF LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD OF QUASI-CONSTANT CURVATURE

2012 ◽  
Vol 19 (4) ◽  
pp. 327-335
Author(s):  
Dae Ho Jin
Keyword(s):  
Riemannian Manifold ◽  
Constant Curvature ◽  
Lightlike Submanifolds

scholarly journals Half lightlike submanifolds of a semi-Riemannian manifold of quasi-constant curvature

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1737-1745
Author(s):  
Dae Jin ◽  
Jae Lee
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Constant Curvature ◽  
Curvature Vector ◽  
Conformal Killing ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Screen Distribution ◽  
Lightlike Submanifolds

We study the geometry of half lightlike submanifolds (M,g,S(TM), S(TM?)) of a semi-Riemannian manifold (M~,g~) of quasi-constant curvature subject to the following conditions; (1) the curvature vector field ? of M~ is tangent to M, (2) the screen distribution S(TM) of M is either totally geodesic or totally umbilical in M, and (3) the co-screen distribution S(TM?) of M is a conformal Killing distribution.

On the non-regularity of tangent sphere bundles

1978 ◽  
Vol 82 (1-2) ◽  
pp. 13-17 ◽  
Author(s):  
David E. Blair
Keyword(s):  
Riemannian Manifold ◽  
Large Class ◽  
Constant Curvature ◽  
Positive Constant ◽  
Contact Structure ◽  
Compact Riemannian Manifold ◽  
Contact Structures ◽  
Sphere Bundle ◽  
Contact Manifolds ◽  
Tangent Sphere

SynopsisClassically the tangent sphere bundles have formed a large class of contact manifolds; their contact structures are not in general regular, however. Specifically we prove that the natural contact structure on the tangent sphere bundle of a compact Riemannian manifold of non-positive constant curvature is not regular.

TOPONOGOV-TYPE AREA COMPARISON THEOREM OF 2-DIMENSIONAL MANIFOLDS

2013 ◽  
Vol 15 (03) ◽  
pp. 1350007
Author(s):  
XIAOLE SU ◽  
HONGWEI SUN ◽  
YUSHENG WANG
Keyword(s):  
Riemannian Manifold ◽  
Comparison Theorem ◽  
Constant Curvature ◽  
Dimensional Manifold ◽  
Geodesic Triangle ◽  
Type Area ◽  
Simply Connected

Let △p1p2p3 be a geodesic triangle on M, a complete 2-dimensional Riemannian manifold of curvature ≥ k, and let [Formula: see text] be its comparison triangle on [Formula: see text] (a complete and simply connected 2-dimensional manifold of constant curvature k). Our main result is that if △p1p2p3 is areable, then its area is not less than that of [Formula: see text].

scholarly journals Submanifolds and the length of the second fundamental tensor

1983 ◽  
Vol 34 (1) ◽  
pp. 1-6
Author(s):  
Thomas Hasanis
Keyword(s):  
Riemannian Manifold ◽  
Constant Curvature ◽  
Positive Constant ◽  
Mean Curvature ◽  
Sufficient Condition ◽  
Fundamental Tensor ◽  
The Mean

AbstractA sufficient condition, for a complete submanifold of a Riemannian manifold of positive constant curvature to be umbilical, is given. The condition will be given by an inequality which is established between the length of the second fundamental tensor and the mean curvature.

ON FINSLER MANIFOLDS WHOSE TANGENT BUNDLE HAS THE g-NATURAL METRIC

2011 ◽  
Vol 08 (07) ◽  
pp. 1593-1610 ◽  
Author(s):  
ESMAEIL PEYGHAN ◽  
AKBAR TAYEBI
Keyword(s):  
Riemannian Manifold ◽  
Constant Curvature ◽  
Positive Constant ◽  
Tangent Bundle ◽  
Contact Structure ◽  
Jacobi Operator ◽  
Riemannian Metric ◽  
Finsler Manifolds ◽  
Almost Contact Structure ◽  
Flat Riemannian Manifold

In this paper, we introduce a Riemannian metric [Formula: see text] and a family of framed f-structures on the slit tangent bundle [Formula: see text] of a Finsler manifold Fn = (M, F). Then we prove that there exists an almost contact structure on the tangent bundle, when this structure is restricted to the Finslerian indicatrix. We show that this structure is Sasakian if and only if Fn is of positive constant curvature 1. Finally, we prove that (i) Fn is a locally flat Riemannian manifold if and only if [Formula: see text], (ii) the Jacobi operator [Formula: see text] is zero or commuting if and only if (M, F) have the zero flag curvature.

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