A natural differential operator on conic spaces

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2011, 2011(Special): 568-577. doi: 10.3934/proc.2011.2011.568

A natural differential operator on conic spaces

Daniel Grieser ^1,

1.	Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany

Received July 2010 Revised January 2011 Published October 2011

Abstract
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Under a Creative Commons license

We introduce the notion of a conic space, as a natural structure on a manifold with boundary, and dene a natural first order differential operator, $c_d_\partial$, acting on boundary values of conic one-forms. Conic structures arise, for example, from resolutions of manifolds with conic singularities, embedded in a smooth ambient space. We show that pull-backs of smooth ambient one-forms to the resolution are cd@-closed, and that this is the only local condition on oneforms that is invariantly dened on conic spaces. The operator $c_d_\partial$ extends to conic Riemannian metrics, and $c_d_\partial$-closed conic metrics have important geometric properties like the existence of an exponential map at the boundary.

Keywords: conic singularity, rescaled tangent bundle, resolution.

Mathematics Subject Classification: Primary: 58J99.

Citation: Daniel Grieser. A natural differential operator on conic spaces. Conference Publications, 2011, 2011 (Special) : 568-577. doi: 10.3934/proc.2011.2011.568

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