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Affine Surfaces Which are Kähler, Para-Kähler, or Nilpotent Kähler

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Abstract

Motivated by the construction of Bach flat neutral signature Riemannian extensions, we study the space of parallel trace-free tensors of type (1, 1) on an affine surface. It is shown that the existence of such a parallel tensor field is characterized by the recurrence of the symmetric part of the Ricci tensor.

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Authors and Affiliations

  1. Consellería de Cultura, Educación e Ordenación Universitaria, Edificio Administrativo San Caetano, 15781, Santiago, Spain

    E. Calviño-Louzao

  2. Faculty of Mathematics, University of Santiago de Compostela, 15782, Santiago, Spain

    E. García-Río & I. Gutiérrez-Rodríguez

  3. Mathematics Department, University of Oregon, Eugene, OR, 97403, USA

    P. Gilkey

  4. Department of Mathematics, IES de Ribadeo Dionisio Gamallo, 27700, Ribadeo, Spain

    R. Vázquez-Lorenzo

Authors
  1. E. Calviño-Louzao
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  2. E. García-Río
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  3. P. Gilkey
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  4. I. Gutiérrez-Rodríguez
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  5. R. Vázquez-Lorenzo
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Corresponding author

Correspondence to E. García-Río.

Additional information

Dedication: In memory of the victims of terrorism Thursday 17 August 2017 (Barcelona Espana), Saturday 12 August 2017 (Charlottesville USA), etc.

Supported by Projects ED431F 2017/03, and MTM2016-75897-P (Spain).

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Calviño-Louzao, E., García-Río, E., Gilkey, P. et al. Affine Surfaces Which are Kähler, Para-Kähler, or Nilpotent Kähler. Results Math 73, 135 (2018). https://doi.org/10.1007/s00025-018-0895-5

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  • DOI: https://doi.org/10.1007/s00025-018-0895-5

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