arXiv subjects

Víctor Manero

Publications and source records attributed to Víctor Manero.

3 recordsLinked to original sources

arXiv2018

Einstein $\mathrm{SU}(3)$ and $\mathrm{G}_2$ structures

We describe a method to obtain $\mathrm{SU}(3)$-structures and $\mathrm{G}_2$-structures on 6 and 7-dimensional manifolds respectively, such that its associated metric is Einstein. More concretely, we have that different classes of $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$-structures, on 5 and 6-dimensional manifolds whose induced metric is Einstein can produce, via warped products, different classes $\mathrm{SU}(3)$ and $\mathrm{G}_2$-structures such that its associated metric is also Einstein.

math.DG↗

arXiv2015

Laplacian flow of closed $G_2$-structures inducing nilsolitons

We study the existence of left invariant closed $G_2$-structures defining a Ricci soliton metric on simply connected nonabelian nilpotent Lie groups. For each one of these $G_2$-structures, we show long time existence and uniqueness of solution for the Laplacian flow on the noncompact manifold. Moreover, considering the Laplacian flow on the associated Lie algebra as a bracket flow on $\R^7$ in a similar way as in [23] we prove that the underlying metrics $g(t)$ of the solution converge smoothly, up to pull-back by time-dependent diffeomorphisms, to a flat metric, uniformly on compact sets in the nilpotent Lie group, as $t$ goes to infinity.

math.DG↗

arXiv2012

Symplectic half-flat solvmanifolds

We classify solvable Lie groups admitting left invariant symplectic half-flat structure. When the Lie group has a compact quotient by a lattice, we show that these structures provide solutions of supersymmetric equations of type IIA.

math.DG↗