RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2001, Volume 69, Issue 1, Pages 36–51 (Mi mz482)

On the Geometry of Lagrangian Submanifolds

V. F. Kirichenko

Moscow State Pedagogical University

Abstract: We prove that a Lagrangian submanifold passes through each point of a symplectic manifold in the direction of arbitrary Lagrangian plane at this point. Generally speaking, such a Lagrangian submanifold is not unique; nevertheless, the set of all such submanifolds in Hermitian extension of a symplectic manifold of dimension greater than 4 for arbitrary initial data contains a totally geodesic submanifold (which we call the $s$-Lagrangian submanifold) if this symplectic manifold is a complex space form. We show that each Lagrangian submanifold in a complex space form of holomorphic sectional curvature equal to $c$ is a space of constant curvature $c/4$. We apply these results to the geometry of principal toroidal bundles.

DOI: https://doi.org/10.4213/mzm482

Full text: PDF file (239 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2001, 69:1, 32–45

Bibliographic databases:

UDC: 514.76
Revised: 22.05.2000

Citation: V. F. Kirichenko, “On the Geometry of Lagrangian Submanifolds”, Mat. Zametki, 69:1 (2001), 36–51; Math. Notes, 69:1 (2001), 32–45

Citation in format AMSBIB
\Bibitem{Kir01} \by V.~F.~Kirichenko \paper On the Geometry of Lagrangian Submanifolds \jour Mat. Zametki \yr 2001 \vol 69 \issue 1 \pages 36--51 \mathnet{http://mi.mathnet.ru/mz482} \crossref{https://doi.org/10.4213/mzm482} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1830981} \zmath{https://zbmath.org/?q=an:0999.53051} \transl \jour Math. Notes \yr 2001 \vol 69 \issue 1 \pages 32--45 \crossref{https://doi.org/10.1023/A:1002887227540} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000168619500004}