Miguel Domínguez Vázquez

PhD students

• Ángel Cidre Díaz, Universidade de Santiago de Compostela, ongoing.

  PhD publications:

  

  • Á. Cidre-Diaz, V. Sanmartín-López: Ricci solitons as submanifolds of complex hyperbolic spaces. arXiv:2407.06999.
• Tomás Otero Casal, Universidade de Santiago de Compostela, 2024.
  Tomás is now a postdoctoral researcher at Universität Münster.

  PhD thesis: Homogeneous hypersurfaces in symmetric spaces.

  PhD publications:

  

  • J. C. Díaz-Ramos, M. Domínguez-Vázquez, T. Otero: Cohomogeneity one actions on symmetric spaces of noncompact type and higher rank. Adv. Math. 428 (2023), 109165.
  • J. C. Díaz-Ramos, M. Domínguez-Vázquez, T. Otero: Homogeneous hypersurfaces in symmetric spaces. New Trends in Geometric Analysis - Spanish Network of Geometric Analysis 2007-2021, RSME Springer Series, 2023.
  
  
• Alberto Rodríguez Vázquez, Universidade de Santiago de Compostela, 2022.
  Alberto is now a Marie Skłodowska-Curie postdoctoral fellow at Université Libre de Bruxelles.

  PhD thesis: Homogeneous hypersurfaces and totally geodesic submanifolds.

  Alberto was awarded the RSME-BBVA Vicent Caselles prize in 2024 due to the results of his PhD thesis.

  PhD publications:

  

  • A. Rodríguez-Vázquez: Totally geodesic submanifolds in products of rank one symmetric spaces. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), doi:10.2422/2036-2145.202301_012.
  • C. Olmos, A. Rodríguez-Vázquez: Hopf fibrations and totally geodesic submanifolds. J. Eur. Math. Soc., to appear.
  • A. Kollross, A. Rodríguez-Vázquez: Totally geodesic submanifolds in exceptional symmetric spaces. Adv. Math., 418 (2023), 108949.
  • J. C. Díaz-Ramos, M. Domínguez-Vázquez, A. Rodríguez-Vázquez: Homogeneous and inhomogeneous isoparametric hypersurfaces in rank one symmetric spaces. J. Reine Angew. Math. 779 (2021), 189-222.
  • A. Rodríguez-Vázquez: A nonisoparametric hypersurface with constant principal curvatures. Proc. Amer. Math. Soc. 147 (2019), 5417-5420.
• Olga Pérez Barral, Universidade de Santiago de Compostela, 2020.
  Olga is now a high school teacher in Cambados (Spain).

  PhD thesis: Ruled hypersurfaces and homogeneous submanifolds in semi-Riemannian manifolds.

  PhD publications:

  

  • J. C. Díaz-Ramos, M. Domínguez-Vázquez, O. Pérez-Barral: Homogeneous CR submanifolds of complex hyperbolic spaces. Publ. Mat. 67 (2023), 891-912..
  • M. Domínguez-Vázquez, O. Pérez-Barral: Existence and uniqueness of inhomogeneous ruled hypersurfaces with shape operator of constant norm in the complex hyperbolic space. Internat. J. Math., 32 (2021), no. 08, 2150049, 4 pp.
  • O. Pérez-Barral: Some problems on ruled hypersurfaces in nonflat complex space forms. Results Math. 75 (2020), no. 4, 167.
  • M. Domínguez-Vázquez, O. Pérez-Barral: Ruled hypersurfaces with constant mean curvature in complex space forms. J. Geom. Phys. 144 (2019), 121-125.
• Víctor Sanmartín López, Universidade de Santiago de Compostela, 2019.
  Víctor is now Assistant Professor at Universidade de Santiago de Compostela (Spain).

  PhD thesis: Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of non-compact type.

  PhD publications:

  

  • J. Berndt, V. Sanmartín-López: Submanifolds with constant principal curvatures in Riemannian symmetric spaces. Comm. Anal. Geom. 31 (2023), no. 5, 1079-1123.
  • J. C. Díaz-Ramos, M. Domínguez-Vázquez, V. Sanmartín-López: Submanifold geometry in symmetric spaces of noncompact type. São Paulo J. Math. Sci. (Special Section: An Homage to Manfredo P. do Carmo) 15 (2021), 75-110.
  • J. C. Díaz-Ramos, M. Domínguez-Vázquez, V. Sanmartín-López: Isoparametric hypersurfaces in complex hyperbolic spaces. Adv. Math. 314 (2017), 756-805.
  • V. Sanmartín-López: Spacelike isoparametric hypersurfaces. Differential Geom. Appl. 54, Part A (2017), 53-58.
  • J. C. Díaz-Ramos, M. Domínguez-Vázquez, V. Sanmartín-López: Anti-De Sitter spacetimes and isoparametric hypersurfaces in complex space forms. Lorentzian Geometry and Related Topics, Proceedings of the 8th International Meeting on Lorentzian Geometry, GELOMA 2016, Málaga, September 20-23, Springer Proceedings in Mathematics & Statistics 211 (2017), 87-101.
• Cristina Vidal Castiñeira, Universidade de Santiago de Compostela, 2016.
  Cristina is now high school teacher in O Barco de Valdeorras (Spain).

  PhD thesis: Submanifolds in complex projective and hyperbolic planes.

  PhD publications:

  

  • J. C. Díaz-Ramos, M. Domínguez-Vázquez, C. Vidal-Castiñeira: Strongly 2-Hopf hypersurfaces in complex projective and hyperbolic planes. Ann. Mat. Pura Appl. (4) 197 (2018), no. 2, 469-486.
  • J. C. Díaz-Ramos, M. Domínguez-Vázquez, C. Vidal-Castiñeira: Isoparametric submanifolds in two-dimensional complex space forms. Ann. Global Anal. Geom. 53 (2018), no. 2, 205-216.
  • J. C. Díaz-Ramos, M. Domínguez-Vázquez, C. Vidal-Castiñeira: Real hypersurfaces with two principal curvatures in complex projective and hyperbolic planes. J. Geom. Anal. 27 (2017), no. 1, 442-465.
  • J. C. Díaz-Ramos, C. Vidal-Castiñeira: Examples of real hypersurfaces with two principal curvatures in complex projective planes. Int. J. Geom. Meth. Mod. Physics 12 (2015), 1560013 (6 pages).

Research group and projects

• I am a member of the Research Group in Mathematics of the University of Santiago de Compostela, whose coordinator is Antonio Gómez Tato. The previous coordinator was my former mentor and current colleague Eduardo García Río.
• I am also the principal investigator of Project of the National Plan entitled Submanifolds, curvature and geometric equations from the viewpoint of symmetry, with reference PID2022-138988NB-I00, and of the Excellence Project of the Galician Government entitled Geometric and analytic aspects of symmetry, with reference ED431F 2020/04.

Scientific collaborators

• Jürgen Berndt, King's College London, United Kingdom.
  In the first conference Symmetry and shape we celebrated Jürgen Berndt's 60th birthday.
• José Carlos Díaz Ramos, Universidade de Santiago de Compostela, Spain.
  Carlos was my PhD advisor.
• Alberto Enciso, ICMAT-CSIC, Spain.
• David González Álvaro, Universidad Politécnica de Madrid, Spain.
• Claudio Gorodski, Universidade de São Paulo, Brazil.
• Takahiro Hashinaga, Saga University, Japan.
• Andreas Kollross, Universität Stuttgart, Germany.
• José Miguel Manzano, Universidad de Jaén, Spain.
• Lawrence Mouillé, Syracuse University, United States.
• Daniel Peralta Salas, ICMAT-CSIC, Spain.
• Olga Pérez Barral, Consellería de Educación (Xunta de Galicia), Spain.
• Alberto Rodríguez Vázquez, Université Libre de Bruxelles, Belgium.
• Víctor Sanmartín López, Universidade de Santiago de Compostela, Spain.
• Hiroshi Tamaru, Osaka Metropolitan University, Japan.
• Cristina Vidal Castiñeira, Consellería de Educación (Xunta de Galicia), Spain.