An infinite series of compact non-orientable 3-dimensional space forms of constant negative curvature

1983 ◽  
Vol 1 (3) ◽  
pp. 37-49 ◽  
Author(s):  
Emil Molnár
Keyword(s):  
Infinite Series ◽  
Negative Curvature ◽  
Dimensional Space ◽  
Constant Negative Curvature ◽  
Space Forms ◽  
3 Dimensional

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

Triharmonic Riemannian submersions from 3-dimensional space forms

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tomoya Miura ◽  
Shun Maeta
Keyword(s):  
Existence Theorem ◽  
Space Form ◽  
Dimensional Space ◽  
Riemannian Submersion ◽  
Partial Answer ◽  
Riemannian Submersions ◽  
Space Forms ◽  
3 Dimensional

Abstract We show that any triharmonic Riemannian submersion from a 3-dimensional space form into a surface is harmonic. This is an affirmative partial answer to the submersion version of the generalized Chen conjecture. Moreover, a non-existence theorem for f -biharmonic Riemannian submersions is also presented.

scholarly journals Complete surfaces in 3-dimensional space forms

1972 ◽  
Vol 1 (2) ◽  
pp. 275-279
Author(s):  
Takehiro ITOH
Keyword(s):  
Dimensional Space ◽  
Space Forms ◽  
3 Dimensional ◽  
Complete Surfaces

scholarly journals Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms

2007 ◽  
Vol 75 (3) ◽  
pp. 563-581 ◽  
Author(s):  
N. Schmitt ◽  
M. Kilian ◽  
S.-P. Kobayashi ◽  
W. Rossman
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Dimensional Space ◽  
Space Forms ◽  
3 Dimensional

scholarly journals MANNHEIM CURVES IN 3-DIMENSIONAL SPACE FORMS

2013 ◽  
Vol 50 (4) ◽  
pp. 1099-1108 ◽  
Author(s):  
Jin Ho Choi ◽  
Tae Ho Kang ◽  
Young Ho Kim
Keyword(s):  
Dimensional Space ◽  
Space Forms ◽  
3 Dimensional

scholarly journals On biconservative surfaces in $3$-dimensional space forms

2016 ◽  
Vol 24 (5) ◽  
pp. 1027-1045 ◽  
Author(s):  
Dorel Fetcu ◽  
Simona Nistor ◽  
Cezar Oniciuc
Keyword(s):  
Dimensional Space ◽  
Space Forms ◽  
3 Dimensional

scholarly journals Some Symmetric Curvature Conditions on Kenmotsu Manifolds

2018 ◽  
Vol 1 (1) ◽  
pp. 50-56
Author(s):  
Riddhi Jung Shah
Keyword(s):  
Negative Curvature ◽  
Einstein Manifold ◽  
Constant Negative Curvature ◽  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Kenmotsu Manifolds

In this paper, we study locally and globally φ-symmetric Kenmotsu manifolds. In both curvature conditions, it is proved that the manifold is of constant negative curvature - 1 and globally φ-Weyl projectively symmetric Kenmotsu manifold is an Einstein manifold. Finally, we give an example of 3-dimensional Kenmotsu manifold.

BONNET SURFACES IN FOUR-DIMENSIONAL SPACE FORMS

2004 ◽  
Vol 15 (10) ◽  
pp. 981-985
Author(s):  
ATSUSHI FUJIOKA
Keyword(s):  
Mean Curvature ◽  
Dimensional Space ◽  
Curvature Vector ◽  
Reduction Theorem ◽  
Mean Curvature Vector ◽  
Parallel Mean Curvature Vector ◽  
Space Forms ◽  
3 Dimensional ◽  
Flat Normal Bundle ◽  
Parallel Mean Curvature

We study isometric deformations of surfaces in four-dimensional space forms preserving the length of the mean curvature vector. In particular we consider the natural condition, called to be simple, and show that such surfaces with flat normal bundle are Bonnet surfaces in totally geodesic or umbilic 3-dimensional space forms, which is regarded as a generalization of Chen–Yau's reduction theorem for surfaces with parallel mean curvature vector.

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