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Cells of harmonicity

Kolář, Martin (1991)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0742.00067.]We are interested in partial differential equations on domains in 𝒞 n . One of the most natural questions is that of analytic continuation of solutions and domains of holomorphy. Our aim is to describe the domains of holomorphy for solutions of the complex Laplace and Dirac equations. We call them cells of harmonicity. We deduce their properties mostly by examining geometrical properties of the characteristic surface (which is the same for both equations),...

Centroaffine differential geometry and its relations to horizontal submanifolds

Luc Vrancken (2002)

Banach Center Publications

We relate centroaffine immersions f : M ⁿ → ℝ n + 1 to horizontal immersions g of Mⁿ into S n + 1 2 n + 1 ( 1 ) or H n 2 n + 1 ( - 1 ) . We also show that f is an equiaffine sphere, i.e. the centroaffine normal is a constant multiple of the Blaschke normal, if and only if g is minimal.

Certain contact metrics satisfying the Miao-Tam critical condition

Dhriti Sundar Patra, Amalendu Ghosh (2016)

Annales Polonici Mathematici

We study certain contact metrics satisfying the Miao-Tam critical condition. First, we prove that a complete K-contact metric satisfying the Miao-Tam critical condition is isometric to the unit sphere S 2 n + 1 . Next, we study (κ,μ)-contact metrics satisfying the Miao-Tam critical condition.

Characteristic classes for A -bundles

Cap, Andreas, Schichl, Hermann (1996)

Proceedings of the Winter School "Geometry and Physics"

The authors generalize a construction of Connes by defining for an A -bundle E over smooth manifold X and a reduced cyclic cohomology class c a sequence of de Rham cohomology classes c h c k ( E ) . Here A is a convenient algebra, defined by the authors, and E is a locally trivial bundle with standard fibre a right finitely generated projective A -module and bounded A -modules homomorphisms as transition functions.

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