-concircular vector fields and holomorphically projective mappings on Kählerian spaces
-Dirac operator and the Cartan-Kähler theorem
We apply the Cartan-Kähler theorem for the k-Dirac operator studied in Clifford analysis and to the parabolic version of this operator. We show that for the tableaux of the first prolongations of these two operators are involutive. This gives us a new characterization of the set of initial conditions for the 2-Dirac operator.
Kähler manifolds with small eigenvalues of the Dirac operator and a conjecture of Lichnerowicz
We describe all compact spin Kähler manifolds of even complex dimension and positive scalar curvature with least possible first eigenvalue of the Dirac operator.
Kähler manifolds with split tangent bundle
This paper is concerned with compact Kähler manifolds whose tangent bundle splits as a sum of subbundles. In particular, it is shown that if the tangent bundle is a sum of line bundles, then the manifold is uniformised by a product of curves. The methods are taken from the theory of foliations of (co)dimension 1.
Kähler-Einstein metrics singular along a smooth divisor
In this note we discuss some recent and ongoing joint work with Thalia Jeffres concerning the existence of Kähler-Einstein metrics on compact Kähler manifolds which have a prescribed incomplete singularity along a smooth divisor . We shall begin with a general discussion of the problem, and give a rough outline of the “classical” proof of existence in the smooth case, due to Yau and Aubin, where no singularities are prescribed. Following this is a discussion of the geometry of the conical or edge...
Kähler-Hodge Theory for Conformal Complex Cones.
Kashaev's conjecture and the Chern-Simons invariants of knots and links.
Klassifikation 2-dimensionaler Singularitäten mit auflösbaren lokalen Fundamentalgruppen.
Knit products of graded Lie algebras and groups
Let and be graded Lie algebras whose grading is in or , but only one of them. Suppose that is a derivatively knitted pair of representations for , i.e. and satisfy equations which look “derivatively knitted"; then , endowed with a suitable bracket, which mimics semidirect products on both sides, becomes a graded Lie algebra . This graded Lie algebra is called the knit product of and . The author investigates the general situation for any graded Lie subalgebras and of a graded...
Knot polynomials and Vassiliev's invariants.
Kolmogorov problem in and extremal Zolotarev ω-splines [Book]
Kreisscheiben auf Riemannschen Flächen und Eigenwerte des Laplace-Operators.
Kritische Punkte bei der nichtlinearen Tschebyscheff-Approximation.
K-theory from the point of view of C*-algebras and Fredholm representations
These notes represent the subject of five lectures which were delivered as a minicourse during the VI conference in Krynica, Poland, “Geometry and Topology of Manifolds”, May, 2–8, 2004.
K-theory of Boutet de Monvel's algebra
We consider the norm closure 𝔄 of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact manifold X with boundary ∂X. Assuming that all connected components of X have nonempty boundary, we show that K₁(𝔄) ≃ K₁(C(X)) ⊕ ker χ, where χ: K₀(C₀(T*Ẋ)) → ℤ is the topological index, T*Ẋ denoting the cotangent bundle of the interior. Also K₀(𝔄) is topologically determined. In case ∂X has torsion free K-theory, we get K₀(𝔄) ≃ K₀(C(X)) ⊕ K₁(C₀(T*Ẋ)).