Geodesic
Chern--Lashof Absolute Curvature of Complex Submanifolds and Volumes of Grassmann Images
Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 666-675.

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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. 
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A. A. Borisenko; O. V. Leibina. Chern--Lashof Absolute Curvature of Complex Submanifolds and Volumes of Grassmann Images. Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 666-675. http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a2/

[1] D. Ferus, “On the volume of the generalized Gauss map”, Geom. Dedicata, 14:3 (1983), 237–242 | DOI | MR | Zbl

[2] D. Ferus, Totale Absolutkrümmung in Differentialgeometrie und -topologie, Lecture Notes in Math., 66, Springer-Verlag, Berlin–New York, 1968 | MR | Zbl

[3] K. Leichtweiss, “Über eine Art von Krümmungsinvarianten beliebiger Untermannigfaltigkeiten des $n$-dimensionalen euklidischen Raums”, Abh. Math. Sem. Univ. Hamburg, 26 (1963/64), 155–190 | DOI | MR | Zbl

[4] Sh. Kobayasi, K. Nomidzu, Osnovy differentsialnoi geometrii, t. 2, Nauka, M., 1969 | MR | Zbl

[5] A. A. Borisenko, O. V. Leibina, “Klassifikatsiya tochek dvumernykh i trekhmernykh kompleksnykh poverkhnostei po grassmanovu obrazu”, Matem. fizika, analiz, geometriya, 9:4 (2002), 572–594 | MR | Zbl

[6] O. V. Leibina, “O kompleksnykh podmnogoobraziyakh s maksimalnoi golomorfnoi kriviznoi grassmanova obraza”, Matem. zametki, 81:4 (2007), 561–568 | MR | Zbl

[7] J. Erbacher, “Reduction of the codimension of an isometric immersion”, J. Differential Geom., 5 (1971), 333–340 | MR | Zbl