On proper Fredholm submanifolds in a Hilbert space arising from submanifolds in a symmetric space

• KOIKE Naoyuki

  DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE SCIENCE UNIVERSITY OF TOKYO

Abstract

For a given symmetric space of compact type, it is known that a certain Riemannian submersion of a Hilbert space onto the symmetric space is nat-urally defined. In this paper, we describe the principal curvatures and the principal distributions of the inverse image (which becomes a proper Fredholm submanifold) of a curvature adapted submanifold in the symmetric space under this Riemannian submer-sion. The curvature adapted submanifold is minimal if and only if the inverse image is formally minimal in certain sense.

Journal

• Japanese journal of mathematics. New series

  Japanese journal of mathematics. New series 28 (1), 61-80, 2002

  The Mathematical Society of Japan

Keywords

• General Mathematics

Details

• CRID: 1390001205256801280
• NII Article ID: 10015754160
• NII Book ID: AA00690979
• DOI: 10.4099/math1924.28.61
• ISSN: 18613624
• ISSN: 02892316
• MRID: 1933478
• NDL BIB ID: 6342349
• Web Site: http://id.ndl.go.jp/bib/6342349
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I6342349
• Web Site: https://www.jstage.jst.go.jp/article/math1924/28/1/28_1_61/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed