scholarly journals A characterisation of Helices and Cornu spirals in real space forms

1997 ◽  
Vol 56 (1) ◽  
pp. 37-49 ◽  
Author(s):  
J. Arroyo ◽  
M. Barros ◽  
O.J. Garay
Keyword(s):  
Mean Curvature ◽  
Space Form ◽  
Arbitrary Dimension ◽  
Curvature Vector ◽  
Real Space ◽  
Curvature Function ◽  
Mean Curvature Vector ◽  
Space Forms ◽  
Real Space Forms ◽  
Unit Speed

We classify unit speed curves contained in a real space form of arbitrary dimension Nm(c), whose mean curvature vector is proper for the Laplacian. Then we use these results to classify Hopf cylinders of S3 and semi-Riemannian Hopf cylinders of with proper mean curvature function.

scholarly journals Ricci Curvature Inequalities for Skew CR-Warped Product Submanifolds in Complex Space Forms

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1317
Author(s):  
Meraj Ali Khan ◽  
Ibrahim Aldayel
Keyword(s):  
Ricci Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Complex Space ◽  
Space Form ◽  
Curvature Vector ◽  
Mean Curvature Vector ◽  
Space Forms ◽  
Fundamental Goal ◽  
Complex Space Forms

The fundamental goal of this study was to achieve the Ricci curvature inequalities for a skew CR-warped product (SCR W-P) submanifold isometrically immersed in a complex space form (CSF) in the expressions of the squared norm of mean curvature vector and warping functions (W-F). The equality cases were likewise examined. In particular, we also derived Ricci curvature inequalities for CR-warped product (CR W-P) submanifolds. To sustain this study, an example of these submanifolds is provided.

scholarly journals Mean curvature and shape operator of isometric immersions in real-space-forms

1996 ◽  
Vol 38 (1) ◽  
pp. 87-97 ◽  
Author(s):  
Bang-Yen Chen
Keyword(s):  
Riemannian Manifold ◽  
Euclidean Space ◽  
Mean Curvature ◽  
Shape Operator ◽  
Real Space ◽  
Curvature Function ◽  
Isometric Immersions ◽  
Space Forms ◽  
Real Space Forms ◽  
The Mean

According to the well-known Nash's theorem, every Riemannian n-manifold admits an isometric immersion into the Euclidean space En(n+1)(3n+11)/2. In general, there exist enormously many isometric immersions from a Riemannian manifold into Euclidean spaces if no restriction on the codimension is made. For a submanifold of a Riemannian manifold there are associated several extrinsic invariants beside its intrinsic invariants. Among the extrinsic invariants, the mean curvature function and shape operator are the most fundamental ones.

scholarly journals A NEW RESULT ABOUT ALMOST UMBILICAL HYPERSURFACES OF REAL SPACE FORMS

2014 ◽  
Vol 91 (1) ◽  
pp. 145-154 ◽  
Author(s):  
JULIEN ROTH
Keyword(s):  
Space Form ◽  
Short Note ◽  
Real Space ◽  
Round Sphere ◽  
Space Forms ◽  
Compact Hypersurface ◽  
Geodesic Spheres ◽  
Real Space Forms

AbstractIn this short note, we prove that an almost umbilical compact hypersurface of a real space form with almost Codazzi umbilicity tensor is embedded, diffeomorphic and quasi-isometric to a round sphere. Then, we derive a new characterisation of geodesic spheres in space forms.

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