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

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 CONSTANT MEAN CURVATURE HYPERSURFACES IN WARPED PRODUCT SPACES

2007 ◽  
Vol 50 (3) ◽  
pp. 511-526 ◽  
Author(s):  
Luis J. Alías ◽  
Marcos Dajczer
Keyword(s):  
Mean Curvature ◽  
Warped Product ◽  
Constant Mean Curvature ◽  
Complete Riemannian Manifold ◽  
General Situation ◽  
Warped Products ◽  
General Version ◽  
Product Spaces ◽  
Constant Mean Curvature Hypersurfaces ◽  
Warped Product Spaces

AbstractWe study hypersurfaces of constant mean curvature immersed into warped product spaces of the form $\mathbb{R}\times_\varrho\mathbb{P}^n$, where $\mathbb{P}^n$ is a complete Riemannian manifold. In particular, our study includes that of constant mean curvature hypersurfaces in product ambient spaces, which have recently been extensively studied. It also includes constant mean curvature hypersurfaces in the so-called pseudo-hyperbolic spaces. If the hypersurface is compact, we show that the immersion must be a leaf of the trivial totally umbilical foliation $t\in\mathbb{R}\mapsto\{t\}\times\mathbb{P}^n$, generalizing previous results by Montiel. We also extend a result of Guan and Spruck from hyperbolic ambient space to the general situation of warped products. This extension allows us to give a slightly more general version of a result by Montiel and to derive height estimates for compact constant mean curvature hypersurfaces with boundary in a leaf.

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