EXTREMAL LORENTZIAN SURFACES WITH NULL $r$-PLANAR GEODESICS IN SPACE FORMS

• HASEGAWA KAZUYUKI

  Faculty of Teacher Education, Institute of Human and Social Sciences, Kanazawa University

• MIURA KOUHEI

  Department of Mathematics, Faculty of Science, Tokyo University of Science

Bibliographic Information

Other Title

• Extremal Lorentzian surfaces with null τ-planar geodesics in space forms

Abstract

We show a congruence theorem for oriented Lorentzian surfaces with horizontal reflector lifts in pseudo-Riemannian space forms of neutral signature. As a corollary, a characterization theorem is obtained for the Lorentzian Boruvka spheres, that is, a full real analytic null $r$-planar geodesic immersion with vanishing mean curvature vector field is locally congruent to the Lorentzian Boruvka sphere in a 2$r$-dimensional space form of neutral signature.

Journal

• Tohoku Mathematical Journal, Second Series

  Tohoku Mathematical Journal, Second Series 67 (4), 611-634, 2015-12-30

  Mathematical Institute, Tohoku University

Keywords

• Extremal Lorentzian surfaces
• higher fundamental forms
• reflector lifts
• Boruvka spheres

Details

• CRID: 1391131406293563904
• NII Article ID: 130007961946
• NII Book ID: AA00863942
• DOI: 10.2748/tmj/1450798076
• ISSN: 2186585X
• ISSN: 00408735
• Web Site: http://hdl.handle.net/2297/46778
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed