On equivalence of two constructions of invariants of Lagrangian submanifolds

2000 ◽  
Vol 195 (2) ◽  
pp. 371-415 ◽  
Author(s):  
Darko Milinković
Keyword(s):  
Lagrangian Submanifolds

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.

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

scholarly journals Generating Forms of Lagrangian Submanifolds

1972 ◽  
Vol 22 (3) ◽  
pp. 267-275 ◽  
Author(s):  
J. Śniatycki ◽  
W. Tulczyjew
Keyword(s):  
Lagrangian Submanifolds
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