scholarly journals Transforms for minimal surfaces in 5-dimensional space forms

2017 ◽  
Vol 102 (116) ◽  
pp. 241-246 ◽  
Author(s):  
Makoto Sakaki
Keyword(s):  
Minimal Surface ◽  
Minimal Surfaces ◽  
Space Form ◽  
Dimensional Space ◽  
Space Forms

For a minimal surface in a 5-dimensional space form, we give transforms to get another minimal surface in another 5-or 4-dimensional space form.

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 Harmonic morphisms and conformal foliations by geodesics of three-dimensional space forms

1991 ◽  
Vol 51 (1) ◽  
pp. 118-153 ◽  
Author(s):  
Paul Baird ◽  
John C. Wood
Keyword(s):  
Space Form ◽  
Holomorphic Mapping ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Classification ◽  
Harmonic Morphisms ◽  
Connected Space ◽  
Space Forms ◽  
Simply Connected ◽  
Three Dimensional Space

AbstractA complete classification is given of harmonic morphisms to a surface and conformal foliations by geodesics, with or without isolated singularities, of a simply-connected space form. The method is to associate to any such a holomorphic map from a Riemann surface into the space of geodesics of the space form. Properties such as nonintersecting fibres (or leaves) are translated into conditions on the holomorphic mapping which show it must have a simple form corresponding to a standard example.

scholarly journals PSEUDO-PARALLEL KAEHLERIAN SUBMANIFOLDS IN COMPLEX SPACE FORMS

2020 ◽  
pp. 321
Author(s):  
Ahmet Yildiz
Keyword(s):  
Sectional Curvature ◽  
Fundamental Form ◽  
Complex Space ◽  
Space Form ◽  
Dimensional Space ◽  
Second Fundamental Form ◽  
Holomorphic Sectional Curvature ◽  
Space Forms ◽  
Totally Geodesic ◽  
Complex Space Forms

Let $\tilde{M}^{m}(c)$ be a complex $m$-dimensional space form of holomorphic sectional curvature $c$ and $M^{n}$ be a complex $n$-dimensional Kaehlerian submanifold of $\tilde{M}^{m}(c).$ We prove that if $M^{n}$ is pseudo-parallel and $Ln-\frac{1}{2}(n+2)c\geqslant 0$ then $M$ $^{n}$ is totally geodesic. Also, we study Kaehlerian submanifolds of complex space form with recurrent second fundamental form.

Description of a 3-periodic minimal surface family with trigonal symmetry

1994 ◽  
Vol 209 (1) ◽  
Author(s):  
A. Fogden
Keyword(s):  
Minimal Surface ◽  
Minimal Surfaces ◽  
Weierstrass Representation ◽  
Systematic Analysis ◽  
Trigonal Symmetry ◽  
Triply Periodic Minimal Surfaces ◽  
Periodic Minimal Surface ◽  
Triply Periodic ◽  
The Family

AbstractA systematic analysis of a family of triply periodic minimal surfaces of genus seven and trigonal symmetry is given. The family is found to contain five such surfaces free from self-intersections, three of which are previously unknown. Exact parametrisations of all surfaces are provided using the Weierstrass representation.

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