GIUV2023-553
Our work is developed within the field of discovering the influence that curvature (in its different extrinsic and intrinsic facets) has on the geometry, topology and analysis of a range and, reciprocally, in the study of the possible determination of curvature through these properties and in the study of some of these properties caused by physical problems. We specifically focus on the study of Kähler Ricci-flat metrics on tangent bundles, twists of Higgs fields, some special curvatures of Wolf spaces, T-duality, the movement (and the consequent production of singularities) of a subvariety by different extrinsic geometric flows and approaches to the search for weak solutions of the Ricci flow and some of its variants to study peculiar geometric structures, the study of certain types of homogeneous spaces and the determination of certain geometric properties of a space closed by the Laplacian spectrum. It is worth noting the applicability of some of these problems to physics (unified theories), the formation of stable surfaces of some materials and tomography. More specifically, we set the following specific objectives: O1.1 Determination of all Kahler Ricci-flat metrics on the...Our work is developed within the field of discovering the influence that curvature (in its different extrinsic and intrinsic facets) has on the geometry, topology and analysis of a range and, reciprocally, in the study of the possible determination of curvature through these properties and in the study of some of these properties caused by physical problems. We specifically focus on the study of Kähler Ricci-flat metrics on tangent bundles, twists of Higgs fields, some special curvatures of Wolf spaces, T-duality, the movement (and the consequent production of singularities) of a subvariety by different extrinsic geometric flows and approaches to the search for weak solutions of the Ricci flow and some of its variants to study peculiar geometric structures, the study of certain types of homogeneous spaces and the determination of certain geometric properties of a space closed by the Laplacian spectrum. It is worth noting the applicability of some of these problems to physics (unified theories), the formation of stable surfaces of some materials and tomography. More specifically, we set the following specific objectives: O1.1 Determination of all Kahler Ricci-flat metrics on the tangent bundle of rank 2 symmetric spaces and Hermitian symmetric spaces. O1.2 To find new families of G-invariant metrics on the sphere bundles indicated in the introduction, thus converting them into homogeneous Riemannian manifolds, which are less rigid than the Sasaki metric. O1.3 To study the general class of manifolds (possibly Kahler) that we can relate by means of a class of generalised twists in which the compatibility conditions on the connection and the curvature of the bundle are replaced by the canonical connection and the Higgs field equation. O1.4 To study the extension of the Chow & Yang results to a hypothetical generalisation of the Gray result and, in particular, study the properties of the quaternionic bisectional curvature in Wolf spaces. O1.5 To analyse this Strominger-Yau-Zaslow conjecture of mirror symmetry in a series of cases of interest: first on G X R^n semi-direct products, and, in a second phase, to apply these techniques to the case of general nilmanifolds. O1.6 To advance in the study of EBCV geometries and in the search for a broader class of seven-dimensional manifolds in which this family can play a special role. O2.1 To study the rigidity of the Angenent tori and the calculation of the first eigenvalue of the Laplacian associated with the Gaussian density on these tori. O2.2 To obtain Reilly-type formulas of the first eigenvalue of a Laplacian with density in submanifolds of the hyperbolic space. O2.3 To study the (in)stability of the Clifford torus under the VPMCF in the S^3 sphere first and, once understood, conduct similar studies in a higher dimension. O2.4 To study the evolution of non-embedded C^2 Lagrangian tori contained in a sphere, seeking to find type II singularities O2.5 To contribute to the study of translating solitons of a higher codimension and/or with a boundary. O2.6 To study flow through the mean curvature in hyperbolic space with Gaussian density. O.2.7 Use any of the flows transverse to a foliation, or another of this type to study the properties of structures in which the existence of a foliation is essential, among the spaces in which these flows are to be considered would be the EBCVs.
[Read more][Hide]
[Read more][Hide]
- Clasificacion de soluciones especiales y singularidades de flujos geometricos. Determinacion de variedades que admiten estructiuras especiales.
- Extrinsic and Intrinsic Geometric Flows, Geometric Structures on a Manifold and Variational Problems on Manifolds.Geometric flows: evolution of sub-varieties or metrics and study of singularities and eternal solutions.Geometric structures: determination of Ricci-flat Kahler metrics, study of twists.Variational problems: stability of critical points.
| Name | Nature of participation | Entity | Description |
|---|---|---|---|
| ESTHER CABEZAS RIVAS | Director | Universitat de València | |
| Research team | |||
| VICENTE FELIPE MIQUEL MOLINA | Member | Universitat de València | |
| OSCAR MACIA JUAN | Member | Universitat de València | |
| SARA ALBERT NICLOS | Member | Universitat de València | |
| CEDRIC MARTINEZ CAMPOS | Member | Universitat de València | |
| MARIA CARMEN DOMINGO JUAN | Collaborator | Universitat de València | |
| VICENTE PALMER ANDREU | Collaborator | Universitat Jaume I | full university professor |
| JOAQUIN GUAL ARNAU | Collaborator | Universitat Jaume I | full university professor |
| JOSE SALVADOR MOLL CEBOLLA | Collaborator | Universitat de València | |
| MARYAM SHARIFI DELCHEH | Collaborator | Universitat de València - Estudi General | UVEG PhD student |
| VICENT GIMENO GARCIA | Collaborator | Universitat Jaume I | tenured university professor |
- -
- flujos geométrico; estructura geométrica; problema variaciones
