16 citations · 42 across the 17 of their papers we have counts for
17 papers · 1 filter
The structure of homogeneous Riemannian manifolds with nullity
Antonio J. Di Scala, Carlos E. Olmos, Francisco Vittone
We find new conditions that the existence of nullity of the curvature tensor of an irreducible homogeneous space imposes on the Lie algebra of and on the…
Spherical 2-Dupin submanifolds
Antonio J. Di Scala, Guilherme Machado de Freitas
We show that every spherical 2-Dupin submanifold that is not a hypersurface is conformally congruent to the standard embedding of the real, complex, quaternionic or octonionic proj…
Kahler submanifolds and the Umehara algebra
Xiaoliang Cheng, Antonio J. Di Scala, Yuan Yuan
We show that an indefinite Euclidean complex space is not a relative of an indefinite non-flat complex space form. We further study whether two compact Fubini-Study spaces are rela…
Mok's characteristic varieties and the normal holonomy group
Antonio J. Di Scala, Francisco Vittone
In this paper we complete the study of the normal holonomy groups of complex submanifolds (non nec. complete) of Cn or CPn. We show that irreducible but non transitive normal holon…
On the extendability of parallel sections of linear connections
Antonio J. Di Scala, Gianni Manno
Let be a vector bundle over a simply connected manifold and a linear connection in . Let be a -parallel section of defined o…
Killing vector fields of constant length on compact hypersurfaces
Antonio J. Di Scala
We show that if a compact hypersurface , , admits a non zero Killing vector field of constant length then is even and is diffeomorp…
Codimension reduction in symmetric spaces
Antonio J. Di Scala, Francisco Vittone
In this paper we give a short geometric proof of a generalization of a well-known result about reduction of codimension for submanifolds of Riemannian symmetric spaces.
Conformal holonomy, symmetric spaces, and skew symmetric torsion
Jesse Alt, Antonio J. Di Scala, Thomas Leistner
We consider the question: can the isotropy representation of an irreducible pseudo-Riemannian symmetric space be realized as a conformal holonomy group? Using recent results of Cap…
Corrigendum for "A geometric proof of the Karpelevich-Mostow theorem"
Antonio J. Di Scala, Carlos Olmos
Corollary 2.3 in our paper "A geometric proof of the Karpelevich-Mostow theorem", Bull. Lond. Math. Soc. 41 (2009), no. 4, 634-638, is false. Here we give a counterexample and show…
Kaehler immersions of homogeneous Kaehler manifolds into complex space forms
Antonio J. Di Scala, Andrea Loi, Hideyuki Ishi
In this paper we study the homogeneous Kaehler manifolds (h.K.m.) which can be Kaehler immersed into finite or infinite dimensional complex space forms. On one hand we completely c…
Embedding almost-complex manifolds in almost-complex Euclidean spaces
Antonio J. Di Scala, Daniele Zuddas
We show that any compact almost-complex manifold of complex dimension m can be pseudo-holomorphically embedded in R^(6m) equipped with a suitable almost-complex structure.
Quasi-Kähler Chern-flat manifolds and complex 2-step nilpotent Lie algebras
Antonio J. Di Scala, Jorge Lauret, Luigi Vezzoni
The study of quasi-Kähler Chern-flat almost Hermitian manifolds is strictly related to the study of anti-bi-invariant almost complex Lie algebras. In the present paper we show that…
Complex submanifolds of almost complex Euclidean spaces
Antonio J. Di Scala, Luigi Vezzoni
We prove that a compact Riemann surface can be realized as a pseudo-holomorphic curve of , for some almost complex structure if and only if it is an elliptic…
Connected subgroups of SO(2,n) acting irreducibly on
Antonio J. Di Scala, Thomas Leistner
We classify all connected subgroups of SO(2,n) that act irreducibly on . Apart from itself these are , , if even, $S^1\cdot SO(1,n/2)…
Gray identities, canonical connection and integrability
Antonio J. Di Scala, Luigi Vezzoni
We characterize quasi Kähler manifolds whose curvature tensor associated to the canonical Hermitian connection satisfies the first Bianchi identity. This condition is related with…
A geometric proof of the Karpelevich-Mostow's theorem
Antonio J. Di Scala, Carlos Olmos
In this paper we give a geometric proof of the Karpelevich's theorem that asserts that a semisimple Lie subgroup of isometries, of a symmetric space of non compact type, has a tota…
Irreducibly acting subgroups of $Gl(n,\rr)$
Antonio J. Di Scala, Thomas Leistner, Thomas Neukirchner
In this note we prove the following three algebraic facts which have applications in the theory of holonomy groups and homogeneous spaces: Any irreducibly acting connected subgroup…