Rigidity of complete hypersurfaces in warped product spaces via higher order mean curvatures

2016 ◽  
Vol 57 (2) ◽  
pp. 391-405 ◽  
Author(s):  
Cícero P. Aquino ◽  
Jogli G. Araújo ◽  
Henrique F. de Lima
Keyword(s):  
Warped Product ◽  
Higher Order ◽  
Product Spaces ◽  
Higher Order Mean Curvatures ◽  
Warped Product Spaces ◽  
Complete Hypersurfaces

scholarly journals A Sharp Height Estimate for Compact Hypersurfaces with Constant k-Mean Curvature in Warped Product Spaces

2014 ◽  
Vol 58 (2) ◽  
pp. 403-419 ◽  
Author(s):  
Sandra C. García-Martínez ◽  
Debora Impera ◽  
Marco Rigoli
Keyword(s):  
Mean Curvature ◽  
Warped Product ◽  
Higher Order ◽  
Product Spaces ◽  
Height Estimate ◽  
Higher Order Mean Curvature ◽  
Warped Product Spaces

AbstractIn this paper we obtain a sharp height estimate concerning compact hypersurfaces immersed into warped product spaces with some constant higher-order mean curvature and whose boundary is contained in a slice. We apply these results to draw topological conclusions at the end of the paper.

scholarly journals Warped product spaces with Ricci conditions

2017 ◽  
Vol 41 ◽  
pp. 1365-1375
Author(s):  
Sang Deok LEE ◽  
Byung Hak KIM ◽  
Jin Hyuk CHOI
Keyword(s):  
Warped Product ◽  
Product Spaces ◽  
Warped Product Spaces

scholarly journals Geodesic motion in the neighbourhood of submanifolds embedded in warped product spaces

2008 ◽  
Vol 40 (6) ◽  
pp. 1341-1351 ◽  
Author(s):  
Fábio Dahia ◽  
Carlos Romero ◽  
Lúcio F. P. da Silva ◽  
Reza Tavakol
Keyword(s):  
Warped Product ◽  
Geodesic Motion ◽  
Product Spaces ◽  
Warped Product Spaces

scholarly journals QUINTESSENTIAL INFLATION FROM 5D WARPED PRODUCT SPACES ON A DYNAMICAL FOLIATION

2008 ◽  
Vol 23 (16) ◽  
pp. 1213-1221 ◽  
Author(s):  
LUCIO FABIO P. DA SILVA ◽  
JOSÉ EDGAR MADRIZ AGUILAR
Keyword(s):  
Scalar Field ◽  
Equation Of State ◽  
Warped Product ◽  
Scalar Potential ◽  
Accelerated Expansion ◽  
Vacuum Equation ◽  
Product Spaces ◽  
Inflationary Scenario ◽  
Warped Product Spaces ◽  
The Universe

Assuming the existence of a 5D purely kinetic scalar field on the class of warped product spaces we investigate the possibility of mimic both an inflationary and a quintessential scenarios on 4D hypersurfaces, by implementing a dynamical foliation on the fifth coordinate instead of a constant one. We obtain that an induced chaotic inflationary scenario with a geometrically induced scalar potential and an induced quasi-vacuum equation of state on 4D dynamical hypersurfaces is possible. While on a constant foliation, the universe can be considered as matter-dominated today, in a family of 4D dynamical hypersurfaces, the universe can be passing period of accelerated expansion with a deceleration parameter nearly -1. This effect of the dynamical foliation results negligible at the inflationary epoch allowing for a chaotic inflationary scenario and becomes considerable at the present epoch allowing a quintessential scenario.

scholarly journals UNIQUENESS OF COMPLETE HYPERSURFACES WITH BOUNDED HIGHER ORDER MEAN CURVATURES IN SEMI-RIEMANNIAN WARPED PRODUCTS

2011 ◽  
Vol 54 (1) ◽  
pp. 201-212 ◽  
Author(s):  
C. P. AQUINO ◽  
H. F. DE LIMA
Keyword(s):  
Steady State ◽  
Maximum Principle ◽  
Higher Order ◽  
Hyperbolic Type ◽  
Warped Products ◽  
Higher Order Mean Curvatures ◽  
Uniqueness Results ◽  
State Type ◽  
Type Spaces ◽  
Complete Hypersurfaces

AbstractIn this paper, we deal with complete hypersurfaces immersed with bounded higher order mean curvatures in steady state-type spacetimes and in hyperbolic-type spaces. By applying a generalised maximum principle for the Yau's square operator [11], we obtain uniqueness results in each of these ambient spaces.

scholarly journals ON WARPED PRODUCT SPACES WITH A CERTAIN RICCI CONDITION

2013 ◽  
Vol 50 (5) ◽  
pp. 1683-1691 ◽  
Author(s):  
Byung Hak Kim ◽  
Sang Deok Lee ◽  
Jin Hyuk Choi ◽  
Young Ok Lee
Keyword(s):  
Warped Product ◽  
Product Spaces ◽  
Warped Product Spaces
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