scholarly journals A characterization of Riemannian manifolds of constant curvature

1973 ◽  
Vol 8 (1) ◽  
pp. 103-106 ◽  
Author(s):  
Richard Holzsager
Keyword(s):  
Constant Curvature ◽  
Riemannian Manifolds

scholarly journals A Note on the Characterization of Two-Dimensional Quasi-Einstein Manifolds

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2013
Author(s):  
Gabriel Bercu
Keyword(s):  
Constant Curvature ◽  
Riemannian Manifolds ◽  
Warped Product ◽  
Product Type ◽  
Two Dimensional ◽  
Einstein Manifolds ◽  
Local Coordinates ◽  
Elementary Methods

In this article, we aim to introduce new classes of two-dimensional quasi-Einstein pseudo-Riemannian manifolds with constant curvature. We also give a classification of 2D quasi-Einstein manifolds of warped product type working in local coordinates. All the results are obtained by elementary methods.

scholarly journals A characterization of complete Riemannian manifolds minimally immersed in the unit sphere

1993 ◽  
Vol 131 ◽  
pp. 127-133 ◽  
Author(s):  
Qing-Ming Cheng
Keyword(s):  
Riemannian Manifold ◽  
Fundamental Form ◽  
Riemannian Manifolds ◽  
Unit Sphere ◽  
Second Fundamental Form ◽  
Clifford Torus ◽  
Veronese Surface ◽  
The Second Fundamental Form ◽  
Complete Riemannian Manifolds

Let Mn be an n-dimensional Riemannian manifold minimally immersed in the unit sphere Sn+p (1) of dimension n + p. When Mn is compact, Chern, do Carmo and Kobayashi [1] proved that if the square ‖h‖2 of length of the second fundamental form h in Mn is not more than , then either Mn is totallygeodesic, or Mn is the Veronese surface in S4 (1) or Mn is the Clifford torus .In this paper, we generalize the results due to Chern, do Carmo and Kobayashi [1] to complete Riemannian manifolds.

scholarly journals Characterization of manifolds of constant curvature by spherical curves

2019 ◽  
Vol 199 (1) ◽  
pp. 217-229 ◽  
Author(s):  
Luiz C. B. da Silva ◽  
José D. da Silva
Keyword(s):  
Constant Curvature
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