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JOURNALS // Matematicheskie Zametki // Archive
Mat. Zametki, 2007 Volume 81, Issue 5, Pages 666–675 (Mi mzm3711)
Chern–Lashof Absolute Curvature of Complex Submanifolds and Volumes of Grassmann Images

A. A. Borisenko, O. V. Leibina

V. N. Karazin Kharkiv National University

Abstract: We introduce an analog of the Chern–Lashof absolute curvature for complex submanifolds in complex Euclidean spaces. A relation between this curvature and the volume of the Grassmann image of the submanifold is established.

Keywords: complex submanifold, Grassmann image, Chern–Lashof absolute curvature, total curvature, Riemannian metric, complex projective space.

UDC: 514

Received: 13.02.2004
Revised: 23.05.2005

DOI: 10.4213/mzm3711


 English version: Mathematical Notes, 2007, 81:5, 596–604

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© Steklov Math. Inst. of RAS, 2025