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On the Extrinsic Principal Directions and Curvatures of Lagrangian Submanifolds

by 1,† and 2,*,†
1
Department of Mathematics, KU Leuven, Celestijnenlaan 200B-Box 2400, 3001 Leuven, Belgium
2
PiT and CiT, Department of Mathematics, KU Leuven, Celestijnenlaan 200B-Box 2400, 3001 Leuven, Belgium
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(9), 1533; https://doi.org/10.3390/math8091533
Received: 31 July 2020 / Revised: 25 August 2020 / Accepted: 4 September 2020 / Published: 8 September 2020
(This article belongs to the Special Issue Inequalities in Geometry and Applications)
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. View Full-Text
Keywords: extrinsic principal tangential directions; principal first normal directions; Lagrangian submanifolds extrinsic principal tangential directions; principal first normal directions; Lagrangian submanifolds
MDPI and ACS Style

Moruz, M.; Verstraelen, L. On the Extrinsic Principal Directions and Curvatures of Lagrangian Submanifolds. Mathematics 2020, 8, 1533. https://doi.org/10.3390/math8091533

AMA Style

Moruz M, Verstraelen L. On the Extrinsic Principal Directions and Curvatures of Lagrangian Submanifolds. Mathematics. 2020; 8(9):1533. https://doi.org/10.3390/math8091533

Chicago/Turabian Style

Moruz, Marilena, and Leopold Verstraelen. 2020. "On the Extrinsic Principal Directions and Curvatures of Lagrangian Submanifolds" Mathematics 8, no. 9: 1533. https://doi.org/10.3390/math8091533

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