Hamiltonian-minimal Lagrangian submanifolds in Kaehler manifolds with symmetries

2007 ◽  
Vol 67 (3) ◽  
pp. 865-882 ◽  
Author(s):  
Yuxin Dong
Keyword(s):  
Lagrangian Submanifolds ◽  
Kaehler Manifolds

scholarly journals Upper bounds for Ricci curvatures for submanifolds in Bochner-Kaehler manifolds

2020 ◽  
Vol 51 (1) ◽  
Author(s):  
Mehraj Ahmad Lone ◽  
Yoshio Matsuyama ◽  
Falleh R. Al-Solamy ◽  
Mohammad Hasan Shahid ◽  
Mohammed Jamali
Keyword(s):  
Ricci Curvature ◽  
Riemannian Space ◽  
Space Form ◽  
Lagrangian Submanifolds ◽  
Upper Bounds ◽  
Kaehler Manifolds ◽  
Slant Submanifolds ◽  
Arbitrary Codimension ◽  
The Relationship ◽  
Algebraic Technique

Chen established the relationship between the Ricci curvature and the squared norm of meancurvature vector for submanifolds of Riemannian space form with arbitrary codimension knownas Chen-Ricci inequality. Deng improved the inequality for Lagrangian submanifolds in complexspace form by using algebraic technique. In this paper, we establish the same inequalitiesfor different submanifolds of Bochner-Kaehler manifolds. Moreover, we obtain improvedChen-Ricci inequality for Kaehlerian slant submanifolds of Bochner-Kaehler manifolds.

scholarly journals Linear Boundary Port Hamiltonian Systems defined on Lagrangian submanifolds

2020 ◽  
Vol 53 (2) ◽  
pp. 7734-7739
Author(s):  
Bernhard Maschke ◽  
Arjan van der Schaft
Keyword(s):  
Hamiltonian Systems ◽  
Lagrangian Submanifolds ◽  
Linear Boundary

On Lagrangian Catenoids

2007 ◽  
Vol 50 (3) ◽  
pp. 321-333 ◽  
Author(s):  
David E. Blair
Keyword(s):  
General Problem ◽  
Lagrangian Submanifolds ◽  
Minimal Submanifold ◽  
Conformally Flat ◽  
Totally Geodesic ◽  
Schouten Tensor ◽  
Multiplicity One

AbstractRecently I. Castro and F.Urbano introduced the Lagrangian catenoid. Topologically, it is ℝ × Sn–1 and its induced metric is conformally flat, but not cylindrical. Their result is that if a Lagrangian minimal submanifold in ℂn is foliated by round (n – 1)-spheres, it is congruent to a Lagrangian catenoid. Here we study the question of conformally flat, minimal, Lagrangian submanifolds in ℂn. The general problem is formidable, but we first show that such a submanifold resembles a Lagrangian catenoid in that its Schouten tensor has an eigenvalue of multiplicity one. Then, restricting to the case of at most two eigenvalues, we show that the submanifold is either flat and totally geodesic or is homothetic to (a piece of) the Lagrangian catenoid.

scholarly journals Semi-invariant Riemannian submersions from nearly Kaehler manifolds

2020 ◽  
Vol 17 (07) ◽  
pp. 2050100
Author(s):  
Rupali Kaushal ◽  
Rashmi Sachdeva ◽  
Rakesh Kumar ◽  
Rakesh Kumar Nagaich
Keyword(s):  
Sufficient Conditions ◽  
Riemannian Submersion ◽  
Horizontal Distribution ◽  
Product Manifold ◽  
Riemannian Submersions ◽  
Kaehler Manifolds ◽  
Necessary And Sufficient ◽  
Nearly Kaehler Manifold ◽  
The Vertical Distribution ◽  
Usual Product

We study semi-invariant Riemannian submersions from a nearly Kaehler manifold to a Riemannian manifold. It is well known that the vertical distribution of a Riemannian submersion is always integrable therefore, we derive condition for the integrability of horizontal distribution of a semi-invariant Riemannian submersion and also investigate the geometry of the foliations. We discuss the existence and nonexistence of semi-invariant submersions such that the total manifold is a usual product manifold or a twisted product manifold. We establish necessary and sufficient conditions for a semi-invariant submersion to be a totally geodesic map. Finally, we study semi-invariant submersions with totally umbilical fibers.

Minimal Lagrangian submanifolds in ℂP 3 and the sinh-Gordon equation

2001 ◽  
Vol 40 (1-4) ◽  
pp. 130-143 ◽  
Author(s):  
Ildefonso Castro ◽  
Luc Vrancken
Keyword(s):  
Gordon Equation ◽  
Lagrangian Submanifolds
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