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Marco Kuehnel

Publications and source records attributed to Marco Kuehnel.

8 recordsLinked to original sources
arXiv2009

On graphical foliations and the global existence of Euler's multiplier

We present an equivalent criterion for the global existence of Euler's multiplier for an integrable one-form taking into account the corresponding codim-1-foliation. In particular, the impact of inseparable leaves is considered. Here, we suppose that the foliation can be reduced to a graph; we also discuss obstructions for this assumption. The properties of this graph are decisive for the global existence of Euler's multiplier. As applications we investigate some special cases in which the graph turns out to look very simple.

math.GT↗
arXiv2009

Ricci-flat Deformations of Holomorphic Vector Bundles

In this paper we give a criterion for a deformation of a hermitian vector bundle to be Ricci-flat. As an application we show that on a Kähler manifold, every deformation of a vector bundle can be made Ricci-flat whereas on some Hopf manifolds, the non-existence of a Ricci-flat deformation is related to non-trivial vector bundles on the universal cover ${\mathbb C}^n\setminus\{0\}$. On a surface with $b_1(X)\not=0$ filtrable Ricci-rigid vector bundles prove to be very special. We apply this to Inoue and Hopf surfaces.

math.AG↗
arXiv2007

On asymptotics of complete Ricci-flat Kähler metrics on open manifolds

Tian and Yau constructed a complete Ricci-flat Kähler metric on the complement of an ample and smooth anticanonical divisor. We inquire into the behaviour of this metric towards the boundary divisor and prove a slow decay rate of the difference to an appropriate explicitely given referential metric.

math.DG↗
arXiv2003

On invariance and Ricci-flatness of Hermitian metrics on open manifolds

We discuss a technique to construct Ricci-flat hermitian metrics on complements of (some) anticanonical divisors of almost homogeneous manifolds and discuss when this metric is complete and Kähler. This construction has a strong interplay with invariance groups of the same dimension as the manifold acting with an open orbit. Lie groups of this type we call divisorial. As an application we can describe compact manifolds admitting a divisorially invariant Kähler metric on an open subset. Finally, we see a connection between the reducibility of the anticanonical divisor and the non-triviality of the Kähler cone on the complement.

math.DG↗
arXiv2003

On the existence of Hermitian-harmonic maps from complete Hermitian to complete Riemannian manifolds

On non-Kähler manifolds the notion of harmonic maps is modified to that of Hermitian harmonic maps in order to be compatible with the complex structure. The resulting semilinear elliptic system is {\it not} in divergence form. The case of noncompact complete preimage and target manifolds is considered. We give conditions for existence and uniqueness of Hermitian-harmonic maps and solutions of the corresponding parabolic system, which observe the non-divergence form of the underlying equations. Numerous examples illustrate the theoretical results and the fundamental difference to harmonic maps.

math.DG↗
arXiv2002

Calabi-Yau-threefolds with Picard number $ρ(X)=2$ and their Kaehler cone II

We prove the rationality of the Kähler cone and the positivity of $c_2(X)$, if $X$ is a Calabi-Yau-threefold with $ρ(X)=2$ and has an embedding into a ${\bb P}^n$-bundle over ${\bb P}^m$ in the cases $(n,m)=(1,3),(3,1)$. The case $(n,m)=(2,2)$ has been done in the first part of this paper. Moreover, if $(n,m)=(3,1)$, we describe the 'other' contraction different from the projection.

math.AG↗
arXiv2001

Calabi-Yau-threefolds with Picard number $ρ(X)=2$ and their Kaehler cone I

We describe properties of the Kähler cone of general Calabi-Yau-threefolds with Picard number $ρ(X)=2$ and prove the rationality of the Kähler cone, if $X$ is a Calabi-Yau-hypersurface in a ${\mathbb P}^2$-bundle over ${\mathbb P}^2$ and $c_3(X)\le -54$. Without the latter assumption we prove the positivity of $c_2(X)$.

math.AG↗