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9 papers · 2 filters
Complete connections on fiber bundles
Matias del Hoyo
Every smooth fiber bundle admits a complete (Ehresmann) connection. This result appears in several references, with a proof on which we have found a gap, that does not seem possibl…
Higgs bundles, the Toledo invariant and the Cayley correspondence
Olivier Biquard, Oscar Garcia-Prada, Roberto Rubio
We define the Toledo invariant of a G-Higgs bundle on a Riemann surface, where G is a real semisimple group of Hermitian type, and we prove a Milnor-Wood type bound for this invari…
Principal actions of stacky Lie groupoids
Henrique Bursztyn, Francesco Noseda, Chenchang Zhu
Stacky Lie groupoids are generalizations of Lie groupoids in which the "space of arrows" of the groupoid is a differentiable stack. In this paper, we consider actions of stacky Lie…
Stable hypersurfaces with zero scalar curvature in Euclidean space
Hilário Alencar, Manfredo do Carmo, Gregório Silva Neto
In this paper we prove some results concerning stability of hypersurfaces in the four dimensional Euclidean space with zero scalar curvature. First we prove there is no complete st…
Cylindricity of complete Euclidean submanifolds with relative nullity
Felippe Soares GuimarÃes, Guilherme Machado De Freitas
We show that a complete Euclidean submanifold with minimal index of relative nullity and Ricci curvature with a certain controlled decay must be a -cylinder. This is a…
A representation for pseudoholomorphic surfaces in spheres
M. Dajczer, Th. Vlachos
We give a local representation for the pseudoholomorphic surfaces in Euclidean spheres in terms of holomorphic data. Similar to the case of the generalized Weierstrass representati…