Generalized Second Fundamental form for Lipschitzian Hypersurfaces by Way of Second Epi Derivatives

1992 ◽  
Vol 35 (4) ◽  
pp. 523-536 ◽  
Author(s):  
Dominikus Noll
Keyword(s):  
Fundamental Form ◽  
Second Fundamental Form ◽  
Convex Hypersurface ◽  
Parallel Surfaces ◽  
Limit Procedure

AbstractUsing second epi derivatives, we introduce a generalized second fundamental form for Lipschitzian hypersurfaces. In the case of a convex hypersurface, our approach leads back to the classical second fundamental form, which is usually obtained from the second fundamental forms of the outer parallel surfaces by means of a limit procedure.

Parallel surfaces in three-dimensional reducible spaces

2013 ◽  
Vol 143 (3) ◽  
pp. 483-491 ◽  
Author(s):  
Giovanni Calvaruso ◽  
Joeri Van der Veken
Keyword(s):  
Fundamental Form ◽  
Three Dimensional ◽  
Second Fundamental Form ◽  
Parallel Second Fundamental Form ◽  
Parallel Surfaces

We completely classify non-degenerate surfaces with parallel second fundamental form in three-dimensional Riemannian and Lorentzian reducible spaces.

LORENTZIAN SYMMETRIC THREE-SPACES AND THE CLASSIFICATION OF THEIR PARALLEL SURFACES

2009 ◽  
Vol 20 (10) ◽  
pp. 1185-1205 ◽  
Author(s):  
G. CALVARUSO ◽  
J. VAN DER VEKEN
Keyword(s):  
Vector Field ◽  
Fundamental Form ◽  
Homogeneous Spaces ◽  
Three Dimensional ◽  
Second Fundamental Form ◽  
Parallel Second Fundamental Form ◽  
Parallel Surfaces ◽  
Riemannian Case ◽  
Lorentzian Homogeneous Spaces

We describe a global model for Lorentzian symmetric three-spaces admitting a parallel null vector field, and classify completely the surfaces with parallel second fundamental form in all Lorentzian symmetric three-spaces. Interesting differences arise with respect to the Riemannian case studied in [2]. Our results complete the classification of parallel surfaces in all three-dimensional Lorentzian homogeneous spaces.

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.

Complete 3-dimensional λ-translators in the Euclidean space ℝ4

2021 ◽  
pp. 1-54
Author(s):  
Zhi Li ◽  
Guoxin Wei ◽  
Gangyi Chen
Keyword(s):  
Euclidean Space ◽  
Fundamental Form ◽  
Second Fundamental Form ◽  
3 Dimensional ◽  
The Second Fundamental Form

In this paper, we obtain the classification theorems for 3-dimensional complete [Formula: see text]-translators [Formula: see text] with constant squared norm [Formula: see text] of the second fundamental form and constant [Formula: see text] in the Euclidean space [Formula: see text].

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