scholarly journals Sphere theorems for Lagrangian and Legendrian submanifolds

2020 ◽  
Vol 59 (4) ◽  
Author(s):  
Jun Sun ◽  
Linlin Sun
Keyword(s):  
Sphere Theorems ◽  
Legendrian Submanifolds

RIGIDITY AND SPHERE THEOREMS FOR SUBMANIFOLDS

1994 ◽  
Vol 48 (2) ◽  
pp. 291-306 ◽  
Author(s):  
Katsuhiro SHIOHAMA ◽  
Hongwei XU
Keyword(s):  
Sphere Theorems

Stability of Biharmonic Legendrian Submanifolds in Sasakian Space Forms

2008 ◽  
Vol 51 (3) ◽  
pp. 448-459 ◽  
Author(s):  
Toru Sasahara
Keyword(s):  
Critical Points ◽  
Harmonic Map ◽  
Biharmonic Maps ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
The Stability ◽  
Biharmonic Map ◽  
Legendrian Submanifolds

AbstractBiharmonic maps are defined as critical points of the bienergy. Every harmonic map is a stable biharmonic map. In this article, the stability of nonharmonic biharmonic Legendrian submanifolds in Sasakian space forms is discussed.

Classification of Casorati ideal Legendrian submanifolds in Sasakian space forms

2020 ◽  
Vol 155 ◽  
pp. 103768 ◽  
Author(s):  
Jae Won Lee ◽  
Chul Woo Lee ◽  
Gabriel-Eduard Vîlcu
Keyword(s):  
Space Forms ◽  
Sasakian Space Forms ◽  
Legendrian Submanifolds

scholarly journals Interval topology in contact geometry

2019 ◽  
Vol 22 (05) ◽  
pp. 1950042
Author(s):  
Vladimir Chernov ◽  
Stefan Nemirovski
Keyword(s):  
Contact Geometry ◽  
Interval Topology ◽  
Legendrian Submanifolds

A topology is introduced on spaces of Legendrian submanifolds and groups of contactomorphisms. The definition is motivated by the Alexandrov topology in Lorentz geometry.

scholarly journals Positive Isotopies of Legendrian Submanifolds and Applications

2016 ◽  
pp. rnw192
Author(s):  
Vincent Colin ◽  
Emmanuel Ferrand ◽  
Petya Pushkar
Keyword(s):  
Legendrian Submanifolds

scholarly journals The Obata sphere theorems on a quaternionic contact manifold of dimension bigger than seven

2017 ◽  
Vol 7 (4) ◽  
pp. 1119-1170
Author(s):  
Stefan Ivanov ◽  
Alexander Petkov ◽  
Dimiter Vassilev
Keyword(s):  
Contact Manifold ◽  
Sphere Theorems

VANISHING AND TOPOLOGICAL SPHERE THEOREMS FOR SUBMANIFOLDS IN A HYPERBOLIC SPACE

2008 ◽  
Vol 19 (07) ◽  
pp. 811-822 ◽  
Author(s):  
HAIPING FU ◽  
HONGWEI XU
Keyword(s):  
Hyperbolic Space ◽  
Measure Theory ◽  
Geometric Measure Theory ◽  
Vanishing Theorem ◽  
Sphere Theorem ◽  
Homology Groups ◽  
Geometric Measure ◽  
Complete Submanifolds ◽  
Negative Constant ◽  
Sphere Theorems

We extend the vanishing and sphere theorems due to Lawson, Simons, Xin, Shiohama and Xu. By using the techniques of calculus of variations in the geometric measure theory, we prove the vanishing theorem for homology groups of submanifolds in the hyperbolic space Hn(c) with negative constant curvature c. Moreover, we obtain a topological sphere theorem for certain complete submanifolds in Hn(c).

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