Involutions with Isolated Fixed Points on Orientable 3-Dimensional Flat Space Forms

1984 ◽  
Vol 285 (1) ◽  
pp. 305 ◽  
Author(s):  
E. Luft ◽  
D. Sjerve
Keyword(s):  
Fixed Points ◽  
Flat Space ◽  
Space Forms ◽  
3 Dimensional

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 f-Biharmonic Curves in the Three-dimensional Para-Sasakian Space Forms

2021 ◽  
pp. 369-379
Author(s):  
Murat Altunbaş
Keyword(s):  
Three Dimensional ◽  
Space Forms ◽  
3 Dimensional ◽  
Sasakian Space Forms ◽  
Sasakian Structures ◽  
Biharmonic Curves

In this paper, we give some characterizations for proper f-biharmonic curves in the para-Bianchi-Cartan-Vranceanu space forms with 3-dimensional para-Sasakian structures.

scholarly journals An integral formula for compact hypersurfaces in space forms and its applications

2003 ◽  
Vol 74 (2) ◽  
pp. 239-248 ◽  
Author(s):  
Luis J. Alías
Keyword(s):  
Scalar Curvature ◽  
Integral Formula ◽  
Flat Space ◽  
Gauss Map ◽  
Ambient Space ◽  
Geodesic Ball ◽  
Space Forms ◽  
Geodesic Spheres

AbstractIn this paper we establish an integral formula for compact hypersurfaces in non-flat space forms, and apply it to derive some interesting applications. In particular, we obtain a characterization of geodesic spheres in terms of a relationship between the scalar curvature of the hypersurface and the size of its Gauss map image. We also derive an inequality involving the average scalar curvature of the hypersurface and the radius of a geodesic ball in the ambient space containing the hypersurface, characterizing the geodesic spheres as those for which equality holds.

scholarly journals 3-dimensional Lorentz space-forms and Seifert fiber spaces

1985 ◽  
Vol 21 (2) ◽  
pp. 231-268 ◽  
Author(s):  
Ravi S. Kulkarni ◽  
Frank Raymond
Keyword(s):  
Lorentz Space ◽  
Space Forms ◽  
3 Dimensional ◽  
Seifert Fiber Spaces

scholarly journals Families of SU(2) representations for mapping cylinders of periodic monodromy

1997 ◽  
Vol 40 (2) ◽  
pp. 383-392
Author(s):  
G. Daskalopoulos ◽  
S. Dostoglou ◽  
R. Wentworth
Keyword(s):  
Fundamental Group ◽  
Fixed Points ◽  
Conjugacy Classes ◽  
Oriented Surface ◽  
3 Dimensional ◽  
Dimensional Mapping

We examine the action of diffeomorphisms of an oriented surface with boundary on the space of conjugacy classes of SU(2) representations of the fundamental group and prove that in the case of a single periodic diffeomorphism the induced action always has fixed points. For the corresponding 3-dimensional mapping cylinders we obtain families of representations parametrized by their value on the longitude of the torus boundary.

scholarly journals Global Embeddings of BTZ and Schwarzschild-ADS Type Black Holes in a Flat Space

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 841 ◽  
Author(s):  
Anton Sheykin ◽  
Dmitry Solovyev ◽  
Sergey Paston
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cosmological Constant ◽  
Isometric Embedding ◽  
Flat Space ◽  
Ambient Space ◽  
Spherically Symmetric ◽  
Btz Black Hole ◽  
3 Dimensional ◽  
Negative Cosmological Constant

We study the problem of construction of global isometric embedding for spherically symmetric black holes with negative cosmological constant in various dimensions. Firstly, we show that there is no such embedding for 4D RN-AdS black hole in 6D flat ambient space, completing the classification which we started earlier. Then we construct an explicit embedding of non-spinning BTZ black hole in 6D flat ambient space. Using this embedding as an anzats, we then construct a global explicit embedding of d-dimensional Schwarzschild-AdS black hole in a flat ( d + 3 ) -dimensional ambient space.

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