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Energy functions on moduli spaces of flat surfaces with erasing forest
This paper follows on from Nguyen (Geom Funct Anal 20(1):192–228,
2010 ), in which we study flat surfaces with erasing forest, these surfaces are... -
Adiabatic limits, vanishing theorems and the noncommutative residue
In this paper, we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits. As an...
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Kan Replacement of Simplicial Manifolds
We establish a functor Kan from local Kan simplicial manifolds to weak Kan simplicial manifolds. It gives a solution to the problem of extending...
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Intersections of smooth polar unitals with secants are homeomorphic to spheres
In [5] and [6] we proved that (non-empty) sets of absolute points of smooth polarities, i.e. smooth polar unitals, in smooth projective planes of...
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A note on isoparametric generalized quadrangles
We generalize a result of Kramer, see [7, 10.7 and 10.10], on generalized quadrangles associated with isoparametric hypersurfaces of Clifford type to...
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The homeomorphism type of unital-like submanifolds in smooth projective planes
We prove that a compact, connected submanifold of the point space of a smooth projective plane is homeomorphic to a sphere provided that certain...
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Mathematik von außen betrachtet oder Wir nähern uns der Sache ganz behutsam
Gibt es in der Mathematik überhaupt noch etwas zu erforschen? Dieser Frage liegt die Vorstellung zu Grunde, daß, nachdem der Satz des Pythagoras und...
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Implicit Characterizations of Smooth Incidence Geometries
We give a characterization of smooth stable and smooth projective planes in terms of submersion and transversality. Moreover, smooth affine...
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Smooth Hughes planes are classical
We prove that the only compact projective Hughes planes which are smooth projective planes are the classical planes over the complex numbers
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16-Dimensional Smooth Projective Planes with Large Collineation Groups
Smooth projective planes are projective planes defined on smooth manifolds (i.e. the set of points and the set of lines are smooth manifolds) such...
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Smooth Stable Planes
This paper deals with smooth stable planes which generalize the notion of differentiable (affine or projective) planes [
7 ]. It is intended to be the... -
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Smooth projective translation planes
A projective plane is called smooth if both the point space and the line space are smooth manifolds such that the geometric operations are smooth. We...
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Almost convex groups and the eight geometries
If M is a closed Nil geometry 3-manifold then π 1 ( M ) is almost convex with respect to a fairly simple “geometric” generating set. If G is a central...