Holomorphic Lefschetz formula for manifolds with boundary

Lefschetz Fixed Point Formula for Manifolds with Cylindrical Ends

Lefschetz coincidence formula on non-orientable manifolds

We generalize the Lefschetz coincidence theorem to non-oriented manifolds. We use (co-) homology groups with local coefficients. This generalization requires the assumption that one of the considered maps is orientation true.

Corrigendum to: Holomorphic Morse inequalities on manifolds with boundary

— A statement in the paper “Holomorphic Morse inequalities on manifolds with boundary” saying that the holomorphic Morse inequalities for an hermitian line bundle L over X are sharp as long as L extends as semi-positive bundle over a Stein-filling is corrected, by adding certain assumptions. A more general situation is also treated. Résumé. — Nous corrigeons l’énoncé qui affirme que les inégali...

Morse’s index formula in VMO for compact manifolds with boundary

In this paper, we study Vanishing Mean Oscillation vector fields on a compact manifold with boundary. Inspired by the work of Brezis and Niremberg, we construct a topological invariant — the index — for such fields, and establish the analogue of Morse’s formula. As a consequence, we characterize the set of boundary data which can be extended to nowhere vanishing VMO vector fields. Finally, we s...

Strictly Kähler-Berwald manifolds with constant‎ ‎holomorphic sectional curvature

In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎.