The mean curvatures on the tubular hypersurfaces in a space of constant curvature

1989 ◽  
pp. 49-62
Author(s):  
Weihuan Chen
Keyword(s):  
Constant Curvature ◽  
Space Of Constant Curvature ◽  
The Mean

scholarly journals Kinematic formula and tube formula in space of constant curvature

1990 ◽  
Vol 33 (1) ◽  
pp. 79-88
Author(s):  
Sungyun Lee
Keyword(s):  
Euclidean Space ◽  
Euler Characteristic ◽  
Constant Curvature ◽  
Kinematic Formula ◽  
Curvature Invariants ◽  
Space Of Constant Curvature

The Euler characteristic of an even dimensional submanifold in a space of constant curvature is given in terms of Weyl's curvature invariants. A derivation of Chern's kinematic formula in non-Euclidean space is completed. As an application of above results Weyl's tube formula about an odd-dimensional submanifold in a space of constant curvature is obtained.

The relativistic theory of gravitation based on a space of constant curvature

1991 ◽  
Vol 86 (2) ◽  
pp. 111-120 ◽  
Author(s):  
A. A. Logunov ◽  
M. A. Mestvirishvili ◽  
Yu. V. Chugreev
Keyword(s):  
Constant Curvature ◽  
Relativistic Theory ◽  
Space Of Constant Curvature ◽  
Theory Of Gravitation

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.

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