TY - JOUR
T1 - The Gauss-Bonnet theorem and Crofton-type formulas in complex space forms
AU - Abardia, Judit
AU - Gallego, Eduardo
AU - Solanes, Gil
N1 - Funding Information:
∗ Work partially supported by FEDER/MEC grant MTM2006-04353, the Schweiz-erischer Nationalfonds grants PP002-114715, the Ramón y Cajal program and the DIUR from the Generalitat de Catalunya and the ESF. Received May 18, 2009 and in revised form March 19, 2010
PY - 2012/1
Y1 - 2012/1
N2 - We compute the measure with multiplicity of the set of complex planes intersecting a compact domain in any complex space form. The result is given in terms of the so-called hermitian intrinsic volumes. Moreover, we obtain two different versions for the Gauss-Bonnet-Chern formula in complex space forms. One of them gives the Gauss curvature integral in terms of the Euler characteristic, and some hermitian intrinsic volumes. The other one, which is shorter, involves the measure of complex hyperplanes meeting the domain. As a tool, we obtain variation formulas in integral geometry of complex space forms.
AB - We compute the measure with multiplicity of the set of complex planes intersecting a compact domain in any complex space form. The result is given in terms of the so-called hermitian intrinsic volumes. Moreover, we obtain two different versions for the Gauss-Bonnet-Chern formula in complex space forms. One of them gives the Gauss curvature integral in terms of the Euler characteristic, and some hermitian intrinsic volumes. The other one, which is shorter, involves the measure of complex hyperplanes meeting the domain. As a tool, we obtain variation formulas in integral geometry of complex space forms.
UR - https://www.scopus.com/pages/publications/84857687600
U2 - 10.1007/s11856-011-0083-8
DO - 10.1007/s11856-011-0083-8
M3 - Article
AN - SCOPUS:84857687600
SN - 0021-2172
VL - 187
SP - 287
EP - 315
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -