scholarly journals Free elasticae and Willmore tori in warped product spaces

1998 ◽  
Vol 40 (2) ◽  
pp. 265-272 ◽  
Author(s):  
Manuel Barros
Keyword(s):  
Variational Problem ◽  
Critical Points ◽  
Product Space ◽  
Warped Product ◽  
Product Spaces ◽  
De Sitter ◽  
Total Squared Curvature ◽  
Principle Of Symmetric Criticality ◽  
Warped Product Spaces

AbstractWe use the principle of symmetric criticality to connect the Willmore variational problem for surfaces in a warped product space with base a circle, and the free elastica variational problem for curves on its fiber. In addition we obtain a rational oneparameter family of closed helices in the anti De Sitter 3-space which are critical points of the total squared curvature functional. This means they are free elasticae. Also they are spacelike; this allows us to construct a corresponding family of spacelike Willmore tori in a certain kind of spacetime close to the Robertson-Walker spaces.

Compact Einstein multiply warped product space with nonpositive scalar curvature

2019 ◽  
Vol 16 (10) ◽  
pp. 1950162 ◽  
Author(s):  
Buddhadev Pal ◽  
Pankaj Kumar
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Product Space ◽  
Warped Product ◽  
Space Time ◽  
Product Spaces ◽  
Warped Product Spaces ◽  
Friedmann Robertson Walker

In this paper, we characterize the Einstein multiply warped product space with nonpositive scalar curvature. As a result, it is shown that, if [Formula: see text] is Einstein multiple-warped product spaces with compact base and nonpositive scalar curvature, then [Formula: see text] is simply a Riemannian manifold. Next, we apply our result on Generalized Robertson–Walker space-time and Generalized Friedmann–Robertson–Walker space-time.

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 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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