A lower bound for 𝐿₂ length of second fundamental form on minimal hypersurfaces

2021 ◽  
Author(s):  
Jianquan Ge ◽  
Fagui Li
Keyword(s):  
Lower Bound ◽  
Fundamental Form ◽  
Second Fundamental Form ◽  
Minimal Hypersurfaces

EINSTEIN-WEYL DEFORMATIONS AND SUBMANIFOLDS

1996 ◽  
Vol 07 (05) ◽  
pp. 705-719 ◽  
Author(s):  
HENRIK PEDERSEN ◽  
YAT SUN POON ◽  
ANDREW SWANN
Keyword(s):  
Fundamental Form ◽  
Einstein Metrics ◽  
Isometry Group ◽  
Second Fundamental Form ◽  
Local Version ◽  
Positive Ricci Curvature ◽  
Constant Length ◽  
Minimal Hypersurfaces ◽  
Weyl Space ◽  
Weyl Manifold

Motivated by new explicit positive Ricci curvature metrics on the four-sphere which are also Einstein-Weyl, we show that the dimension of the Einstein-Weyl moduli near certain Einstein metrics is bounded by the rank of the isometry group and that any Weyl manifold can be embedded as a hypersurface with prescribed second fundamental form in some Einstein-Weyl space. Closed four-dimensional Einstein-Weyl manifolds are proved to be absolute minima of the L2-norm of the curvature of Weyl manifolds and a local version of the Lafontaine inequality is obtained. The above metrics on the four-sphere are shown to contain minimal hypersurfaces isometric to S1×S2 whose second fundamental form has constant length.

scholarly journals Another class ofwarped product skew CR-submanifolds of Kenmotsu manifolds

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2583-2600 ◽  
Author(s):  
Shyamal Hui ◽  
Tanumoy Pal ◽  
Joydeb Roy
Keyword(s):  
Lower Bound ◽  
Fundamental Form ◽  
Warped Product ◽  
Second Fundamental Form ◽  
Warped Products ◽  
Kenmotsu Manifold ◽  
Equality Case ◽  
Slant Submanifolds ◽  
Kenmotsu Manifolds ◽  
Two Factors

Recently, Naghi et al. [32] studied warped product skew CR-submanifold of the form M1 xf M? of order 1 of a Kenmotsu manifold ?M such that M1 = MT x M?, where MT, M? and M? are invariant, anti-invariant and proper slant submanifolds of ?M. The present paper deals with the study of warped product submanifolds by interchanging the two factors MT and M?, i.e, the warped products of the form M2 xf MT such that M2 = M? x M?. The existence of such warped product is ensured by an example and then we characterize such warped product submanifold. A lower bound of the squared norm of second fundamental form is derived with sharp relation, whose equality case is also considered.

Bi-warped product submanifolds of Kenmotsu manifolds and their applications

2019 ◽  
Vol 16 (01) ◽  
pp. 1950001 ◽  
Author(s):  
Siraj Uddin ◽  
Ali H. Alkhaldi
Keyword(s):  
Lower Bound ◽  
Fundamental Form ◽  
Warped Product ◽  
Second Fundamental Form ◽  
Kenmotsu Manifold ◽  
Equality Case ◽  
The Second Fundamental Form ◽  
Kenmotsu Manifolds

In this paper, we study bi-warped product submanifolds of the form [Formula: see text] in a Kenmotsu manifold. We obtain a lower bound for the squared norm of the second fundamental form of a bi-warped product submanifold such as [Formula: see text], where [Formula: see text] and [Formula: see text] and [Formula: see text] are the warping functions on [Formula: see text]. The equality case is also considered.

scholarly journals Another inequality for skew CR-warped products in Kenmotsu manifolds

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4721-4731
Author(s):  
Siraj Uddin ◽  
Monia Naghi
Keyword(s):  
Lower Bound ◽  
Fundamental Form ◽  
Second Fundamental Form ◽  
Warping Function ◽  
Warped Products ◽  
Equality Case ◽  
The Second Fundamental Form ◽  
Kenmotsu Manifolds ◽  
Cr Submanifolds

In this paper, we study warped products of contact skew-CR submanifolds, called contact skew CR-warped products in Kenmotsu manifolds. We obtain a lower bound relationship between the squared norm of the second fundamental form and the warping function. Furthermore, the equality case is investigated and some applications of derived inequality are given.

scholarly journals First eigenvalue of submanifolds in Euclidean space

2000 ◽  
Vol 24 (1) ◽  
pp. 43-48
Author(s):  
Kairen Cai
Keyword(s):  
Euclidean Space ◽  
Fundamental Form ◽  
Second Fundamental Form ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
The Second Fundamental Form ◽  
Compact Submanifold

We give some estimates of the first eigenvalue of the Laplacian for compact and non-compact submanifold immersed in the Euclidean space by using the square length of the second fundamental form of the submanifold merely. Then some spherical theorems and a nonimmersibility theorem of Chern and Kuiper type can be obtained.

Second Fundamental Form and Mean Curvature

1988 ◽  
pp. 62-73
Author(s):  
Philippe Tondeur
Keyword(s):  
Fundamental Form ◽  
Mean Curvature ◽  
Second Fundamental Form

scholarly journals On the inner geometry of the second fundamental form.

1972 ◽  
Vol 19 (2) ◽  
pp. 129-132 ◽  
Author(s):  
Udo Simon
Keyword(s):  
Fundamental Form ◽  
Second Fundamental Form ◽  
The Second Fundamental Form
Sign in / Sign up

Export Citation Format

Share Document