Results 111 to 120 of about 157 (127)
Isotropic Lagrangian submanifolds in the homogeneous nearly Kähler S3 × S3 [PDF]
Science China Mathematics, 2016 We show that isotropic Lagrangian submanifolds in a 6-dimensional strict nearly Kahler manifold are totally geodesic. Moreover, under some weaker conditions, a complete classification of the J-isotropic Lagrangian submanifolds in the homogeneous nearly Kahler S3 × S3 is also obtained.
Zejun Hu
exaly +2 more sources
Some of the next articles are maybe not open access.
Inequalities on Isotropic Submanifolds in Pseudo-Riemannian Space Forms
International Electronic Journal of Geometry, 2023Spacelike and timelike isotropic submanifolds of pseudo-Riemannian spaces have interesting properties, with important applications in Mathematics and Physics. The article presents inequalities for isotropic spacelike and timelike submanifolds of pseudo-Riemannian space forms and isotropic Lorentzian submanifolds are also considered.
openaire +2 more sources
ON THREE DIMENSIONAL PSEUDO-UMBILICAL ISOTROPIC SUBMANIFOLDS
Demonstratio Mathematica, 1989 exaly +2 more sources
Isotropic submanifolds generated by the Maximum Entropy Principle
AIP Conference Proceedings, 2004We show that the Maximum Entropy Principle (E.T. Jaynes), when considered as a constrained extremization problem, has a natural description in terms of Morse Families of an isotropic (Lagrangian in the finite dimensional case) submanifold of an infinite‐dimensional linear symplectic space.
openaire +1 more source
Symplectic curvature and the arnold form over and isotropic submanifold
Journal of Mathematical Sciences, 1996The authors study Hamiltonian systems in a \(2d\)-dimensional symplectic manifold \((M, \omega)\) having an isotropic (but non-Lagrangian) compact connected invariant \(k\)-dimensional submanifold \(\Lambda\), by means of a Darboux atlas over \(\Lambda\). They define a Darboux coordinate chart over \(\Lambda\) as a domain \(U\subset M\) together with a
Karasev, M. V., Vorobjev, Yu. M.
openaire +1 more source
Isotropic submanifolds with pointwise planar normal sections
Journal of Geometry, 1986Let \(M\) be an \(n\)-dimensional submanifold of a Euclidean \(m\)-space \(E^ m\). For a unit tangent vector t at a point \(p\) in \(M\), the vector \(t\) and the normal space of \(M\) at \(p\) determine an \((m-n+1)\)-dimensional vector space \(E(p,t)\) in \(E^ m\).
Houh, Chorng-Shi, Wang, Guo-Qiang
exaly +2 more sources
Chen Inequalities for Isotropic Submanifolds in Pseudo-Riemannian Space Forms
International Electronic Journal of Geometry, 2023The class of isotropic submanifolds in pseudo-Riemannian manifolds is a distinguished family of submanifolds; they have been studied by several authors. In this article we establish Chen inequalities for isotropic immersions. An example of an isotropic immersion for which the equality case in the Chen first inequality holds is given.
openaire +3 more sources
Linear Connections for Hamiltonian Dynamics over Isotropic Submanifold
1994This paper was stimulated by the investigations in quantum spectral problems. We consider the systems having in a classical limit an isotopic (but non-Lagrangian) compact invariant submanifold, for example: a closed trajectory, low-dimensional torus or topologically more complicated object.
Michael Karasev, Yurij Vorobjev
openaire +1 more source
On Ricci curvature of isotropic and Lagrangian submanifolds in complex space forms
Archiv der Mathematik, 2000Let \((M^{n},g)\) be a Riemannian manifold isometrically immersed in \((\tilde{M}^{m},g).\) Let us denote by \(S,H^{2}\) the Ricci tensor and the squared mean curvature, respectively. In a previous paper [\textit{B.-Y. Chen}, Glasg. Math. J. 41, 33--41 (1999; Zbl 0962.53015)], the author proved the following basic inequality for any submanifold \((M^{n}
openaire +2 more sources
Submanifolds with conformal second fundamental form and isotropic immersions
1992The aim of the present paper is to point out some relationships between the isotropic immersions and the submanifolds with conformal second fundamental form and to give some examples of \(m\)-dimensional submanifolds \((m\geq 3)\) immersed in a space of constant curvature with conformal second fundamental form.
CONSOLE, Sergio, SANINI A.
openaire +2 more sources