scholarly journals Optimal Inequalities Between Distances in Convex Projective Domains

2021 ◽  
Author(s):  
Roland Hildebrand
Keyword(s):  
Optimal Inequalities

Curvature inequalities for C-totally real doubly warped products of locally conformal almost cosymplectic manifolds

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6449-6459 ◽  
Author(s):  
Akram Ali ◽  
Siraj Uddin ◽  
Wan Othman ◽  
Cenap Ozel
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Warped Products ◽  
Equality Case ◽  
Cosymplectic Manifolds ◽  
Almost Cosymplectic Manifold ◽  
Locally Conformal ◽  
Totally Real ◽  
Optimal Inequalities

In this paper, we establish some optimal inequalities for the squared mean curvature in terms warping functions of a C-totally real doubly warped product submanifold of a locally conformal almost cosymplectic manifold with a pointwise ?-sectional curvature c. The equality case in the statement of inequalities is also considered. Moreover, some applications of obtained results are derived.

scholarly journals Optimal Inequalities for Power Means

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Yong-Min Li ◽  
Bo-Yong Long ◽  
Yu-Ming Chu ◽  
Wei-Ming Gong
Keyword(s):  
Power Mean ◽  
Power Means ◽  
Optimal Inequalities

We present the best possible power mean bounds for the productMpα(a,b)M-p1-α(a,b)for anyp>0,α∈(0,1), and alla,b>0witha≠b. Here,Mp(a,b)is thepth power mean of two positive numbersaandb.

Certain inequalities for the Casorati curvatures of submanifolds of generalized (k,μ)-space-forms

2018 ◽  
Vol 13 (02) ◽  
pp. 2050040
Author(s):  
Shyamal Kumar Hui ◽  
Pradip Mandal ◽  
Ali H. Alkhaldi ◽  
Tanumoy Pal
Keyword(s):  
Scalar Curvature ◽  
Space Form ◽  
Space Forms ◽  
Civita Connection ◽  
Metric Connection ◽  
Levi Civita Connection ◽  
Casorati Curvature ◽  
Optimal Inequalities

The paper deals with the study of Casorati curvature of submanifolds of generalized [Formula: see text]-space-form with respect to Levi-Civita connection as well as semisymmetric metric connection and derived two optimal inequalities between scalar curvature and Casorati curvature of such space forms. The equality cases are also considered.

scholarly journals Optimal and Nonoptimal Gronwall Lemmas

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1728
Author(s):  
Daniela Marian ◽  
Sorina Anamaria Ciplea ◽  
Nicolaie Lungu
Keyword(s):  
Upper Bound ◽  
Partial Answer ◽  
Optimal Inequalities

In this paper, we study some optimal inequalities of the Riccati type and of the Bihari type. We also consider nonoptimal inequalities of the Wendorf type. At the same time, we get a partial answer to Problems 5 and 9, formulated by I. A. Rus. This paper is also motivated by the fact that, in many inequalities, the upper bound is not an optimal one.

scholarly journals A tour through δ-invariants: From Nash’s embedding theorem to ideal immersions, best ways of living and beyond

2013 ◽  
Vol 94 (108) ◽  
pp. 67-80 ◽  
Author(s):  
Bang-Yen Chen
Keyword(s):  
Riemannian Manifolds ◽  
Lagrangian Submanifolds ◽  
Embedding Theorem ◽  
The Many ◽  
Optimal Inequalities

First I will explain my motivation to introduce the ?-invariants for Riemannian manifolds. I will also recall the notions of ideal immersions and best ways of living. Then I will present a few of the many applications of ?-invariants in several areas in mathematics. Finally, I will present two optimal inequalities involving ?-invariants for Lagrangian submanifolds obtained very recently in joint papers with F. Dillen, J. Van der Veken and L. Vrancken.

Optimal inequalities for the normalized δ-Casorati curvatures of submanifolds in Kenmotsu space forms

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Chul Woo Lee ◽  
Jae Won Lee ◽  
Gabriel-Eduard Vîlcu
Keyword(s):  
Space Forms ◽  
Optimal Inequalities

AbstractIn this paper, we establish two sharp inequalities for the normalized

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