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On the Extrinsic Principal Directions and Curvatures of Lagrangian Submanifolds

Author

Listed:
  • Marilena Moruz

    (Department of Mathematics, KU Leuven, Celestijnenlaan 200B-Box 2400, 3001 Leuven, Belgium
    These authors contributed equally to this work.)

  • Leopold Verstraelen

    (PiT and CiT, Department of Mathematics, KU Leuven, Celestijnenlaan 200B-Box 2400, 3001 Leuven, Belgium
    These authors contributed equally to this work.)

Abstract

From the basic geometry of submanifolds will be recalled what are the extrinsic principal tangential directions , (first studied by Camille Jordan in the 18seventies), and what are the principal first normal directions , (first studied by Kostadin Trenčevski in the 19nineties), and what are their corresponding Casorati curvatures . For reasons of simplicity of exposition only, hereafter this will merely be done explicitly in the case of arbitrary submanifolds in Euclidean spaces. Then, for the special case of Lagrangian submanifolds in complex Euclidean spaces, the natural relationships between these distinguished tangential and normal directions and their corresponding curvatures will be established.

Suggested Citation

  • Marilena Moruz & Leopold Verstraelen, 2020. "On the Extrinsic Principal Directions and Curvatures of Lagrangian Submanifolds," Mathematics, MDPI, vol. 8(9), pages 1-6, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1533-:d:410405
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