Bihermitian Gray surfaces

Bihermitian Metrics on Hopf Surfaces

Inspired by a construction due to Hitchin [20], we produce strongly bihermitian metrics on certain Hopf complex surfaces, which integrate the locally conformally Kähler metrics found by Gauduchon–Ornea [14]. We also show that the Inoue complex surfaces with b2 = 0 do not admit bihermitian metrics. This completes the classification of the compact complex surfaces admitting strongly bihermitian m...

Bihermitian metrics on Del Pezzo surfaces

Recall that a Del Pezzo surface is defined as an algebraic surface with ample anticanonical bundle K. Ampleness means that the line bundle K has a hermitian metric whose curvature form F is positive, defining a Kähler metric g0. This is the data for our construction – we take a holomorphic section σ of K, and the function f = log ‖σ‖. This function is singular on the zero set of σ (which is an ...

Anti-self-dual Bihermitian Structures on Inoue Surfaces

In this article we show that any hyperbolic Inoue surface (also called InoueHirzebruch surface of even type) admits anti-self-dual bihermitian structures. The same result holds for any of its small deformations as far as its anti-canonical system is nonempty. Similar results are obtained for parabolic Inoue surfaces. Our method also yields a family of anti-self-dual hermitian metrics on any hal...

Alfred Gray Modern Differential Geometry of Curves and Surfaces

Towards joint morphometry of white matter tracts and gray matter surfaces

Morphological studies of anatomical structures play an important role in neuroimaging. For example in the analysis of the circuits connecting sub-cortical areas to the cortical surface one would like to study together gray matter surfaces and white matter tracts ( ber bundles). To the best of our knowledge, there is no generic method to study these objects together. Atlas construction is based ...