scholarly journals A basic inequality for submanifolds in a cosymplectic space form

2003 ◽  
Vol 2003 (9) ◽  
pp. 539-547 ◽  
Author(s):  
Jeong-Sik Kim ◽  
Jaedong Choi
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Sectional Curvature ◽  
Mean Curvature ◽  
Space Form ◽  
The Other ◽  
Space Forms ◽  
Basic Inequality

For submanifolds tangent to the structure vector field in cosymplectic space forms, we establish a basic inequality between the main intrinsic invariants of the submanifold, namely, its sectional curvature and scalar curvature on one side; and its main extrinsic invariant, namely, squared mean curvature on the other side. Some applications, including inequalities between the intrinsic invariantδMand the squared mean curvature, are given. The equality cases are also discussed.

A basic inequality for submanifolds in locally conformal almost cosymplectic manifolds

2002 ◽  
Vol 112 (3) ◽  
pp. 415-423
Author(s):  
Mukut Mani Tripathi ◽  
Jeong-Sik Kim ◽  
Seon-Bu Kim
Keyword(s):  
Basic Inequality ◽  
Cosymplectic Manifolds ◽  
Locally Conformal

scholarly journals A refinement and an exact equality condition for the basic inequality of f-divergences

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4263-4273
Author(s):  
László Horváth ◽  
P Pecaric-Dilda ◽  
Josip Pecaric
Keyword(s):  
Information Theory ◽  
Probability Theory ◽  
Mathematical Statistics ◽  
Basic Inequality ◽  
Equality Condition ◽  
Exact Equality

f-divergences play important role in probability theory, especially in information theory and in mathematical statistics. Remarkable divergences can be found among them. Inequalities for f-divergences are very useful and applicable in information theory. In this paper we give a precise equality condition and a refinement for one of the basic inequalities of f-divergences. The results are illustrated by some applications.

A generalization of a basic inequality of Telyakovskiĭ

2011 ◽  
Vol 37 (3) ◽  
pp. 161-172
Author(s):  
L. Leindler
Keyword(s):  
Basic Inequality
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