TY - JOUR

T1 - The Gauss-Bonnet theorem and Crofton-type formulas in complex space forms

AU - Abardia, Judit

AU - Gallego, Eduardo

AU - Solanes, Gil

PY - 2012/1/1

Y1 - 2012/1/1

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. © 2012 Hebrew University Magnes Press.

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. © 2012 Hebrew University Magnes Press.

U2 - https://doi.org/10.1007/s11856-011-0083-8

DO - https://doi.org/10.1007/s11856-011-0083-8

M3 - Article

VL - 187

SP - 287

EP - 315

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

ER -