A Note on the L2-norm of the Second Fundamental Form of Algebraic Manifolds

Loi, Andrea, and Zedda, Michela. "A Note on the L2-norm of the Second Fundamental Form of Algebraic Manifolds." Serdica Mathematical Journal 35.1 (2010): 67-74. <http://eudml.org/doc/281381>.

@article{Loi2010,
abstract = {2000 Mathematics Subject Classification: 53C42, 53C55.Let M f → CP^n be an algebraic manifold of complex dimension d and let σf be its second fundamental form. In this paper we address the following conjecture, which is the analogue of the one stated by M. Gromov for smooth immersions: ... We prove the conjecture in the following three cases: (i) d = 1; (ii) M is a complete intersection; (iii) the scalar curvature of M is constant.},
author = {Loi, Andrea, Zedda, Michela},
journal = {Serdica Mathematical Journal},
keywords = {Kähler Metrics; Holomorphic Maps Into Projective Space; Algebraic Manifolds; Degree},
language = {eng},
number = {1},
pages = {67-74},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {A Note on the L2-norm of the Second Fundamental Form of Algebraic Manifolds},
url = {http://eudml.org/doc/281381},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Loi, Andrea
AU - Zedda, Michela
TI - A Note on the L2-norm of the Second Fundamental Form of Algebraic Manifolds
JO - Serdica Mathematical Journal
PY - 2010
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 35
IS - 1
SP - 67
EP - 74
AB - 2000 Mathematics Subject Classification: 53C42, 53C55.Let M f → CP^n be an algebraic manifold of complex dimension d and let σf be its second fundamental form. In this paper we address the following conjecture, which is the analogue of the one stated by M. Gromov for smooth immersions: ... We prove the conjecture in the following three cases: (i) d = 1; (ii) M is a complete intersection; (iii) the scalar curvature of M is constant.
LA - eng
KW - Kähler Metrics; Holomorphic Maps Into Projective Space; Algebraic Manifolds; Degree
UR - http://eudml.org/doc/281381
ER -