Examples of 1-codimensional non totally geodesic isometric immersions of pseudo-riemannian space forms with the same positive constant curvature and the same space-like rank

1985 ◽  
pp. 59-73 ◽  
Author(s):  
Marcos Dajczer ◽  
Peter Dombrowski
Keyword(s):  
Constant Curvature ◽  
Positive Constant ◽  
Riemannian Space ◽  
Isometric Immersions ◽  
Space Forms ◽  
Totally Geodesic ◽  
Riemannian Space Forms

On Quasi-Minimal Isometric Immersions into Non-Flat Semi Riemannian Space Forms of Index Two

2019 ◽  
Vol 20 ◽  
pp. 255-265
Author(s):  
Nurettin C. Turgay ◽  
◽  
Alev Kelleci ◽  
Rüya Yeğin Şen ◽  
Elif Özkara Canfes
Keyword(s):  
Riemannian Space ◽  
Isometric Immersions ◽  
Space Forms ◽  
Riemannian Space Forms

Isometric immersions of pseudo-Riemannian space forms

2004 ◽  
Vol 52 (3) ◽  
pp. 241-262 ◽  
Author(s):  
Chen Qing ◽  
Zuo Dafeng ◽  
Cheng Yi
Keyword(s):  
Riemannian Space ◽  
Isometric Immersions ◽  
Space Forms ◽  
Riemannian Space Forms

ON CURVATURE PROPERTIES OF CERTAIN QUASI-EINSTEIN HYPERSURFACES

2012 ◽  
Vol 23 (07) ◽  
pp. 1250073 ◽  
Author(s):  
RYSZARD DESZCZ ◽  
MARIAN HOTLOŚ ◽  
ZERRIN ṢENTÜRK
Keyword(s):  
Constant Curvature ◽  
Riemannian Space ◽  
Warped Product ◽  
Space Forms ◽  
Type Identity ◽  
Space Of Constant Curvature ◽  
Riemannian Space Forms

It is known that the Cartan hypersurfaces of dimension 6, 12 or 24 are non-quasi-Einstein, non-pseudosymmetric, Ricci-pseudosymmetric manifolds. In this paper we investigate quasi-Einstein hypersurfaces in semi-Riemannian space forms satisfying some Walker type identity. Among other things we prove that such hypersurfaces are Ricci-pseudosymmetric manifolds. Using certain result of Magid we construct an example of a quasi-Einstein non-pseudosymmetric Ricci-pseudosymmetric warped product which locally can be realized as a hypersurface in a semi-Riemannian space of constant curvature. In our opinion it is a first example of a hypersurface having the mentioned properties.

scholarly journals Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

2021 ◽  
Author(s):  
Andreas Bernig ◽  
Dmitry Faifman ◽  
Gil Solanes
Keyword(s):  
Riemannian Manifolds ◽  
Riemannian Geometry ◽  
Riemannian Space ◽  
Space Forms ◽  
Type Formula ◽  
Isometric Embeddings ◽  
Curvature Measures ◽  
Riemannian Space Forms

AbstractThe recently introduced Lipschitz–Killing curvature measures on pseudo-Riemannian manifolds satisfy a Weyl principle, i.e. are invariant under isometric embeddings. We show that they are uniquely characterized by this property. We apply this characterization to prove a Künneth-type formula for Lipschitz–Killing curvature measures, and to classify the invariant generalized valuations and curvature measures on all isotropic pseudo-Riemannian space forms.

scholarly journals On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms

2003 ◽  
Vol 96 (2) ◽  
pp. 149-166 ◽  
Author(s):  
Ryszard Deszcz ◽  
Małgorzata Głogowska ◽  
Marian Hotloś ◽  
Leopold Verstraelen
Keyword(s):  
Riemannian Space ◽  
Einstein Metric ◽  
Space Forms ◽  
Riemannian Space Forms
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