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Invariant almost Hermitian structures on the maximal real flag manifold of type π’œ3

  • Ana P. C. Freitas
  • Brian Grajales
  • Ailton R. Oliveira
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Abstract

We study the Gray-Hervella classes of invariant almost Hermitian structures on the maximal real flag manifold of type π’œ3. We first obtain an explicit parametrization of all invariant almost Hermitian structures and establish necessary and sufficient conditions for an invariant almost Hermitian structure to belong to each Gray-Hervella class. For each nonempty class, we give an explicit parametrization of the corresponding set of structures, describe it as a smooth manifold and determine its dimension.

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Cite

BibTeXRIS
BibTeX
@misc{freitas2026invariant,
  title = {{Invariant almost Hermitian structures on the maximal real flag manifold of type $\mathcalA_3$}},
  author = {Ana P. C. Freitas and Brian Grajales and Ailton R. Oliveira},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14044},
  eprint = {2609.14044},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14044},
}
RIS
TY  - UNPB
TI  - Invariant almost Hermitian structures on the maximal real flag manifold of type π’œ_3
AU  - Ana P. C. Freitas
AU  - Brian Grajales
AU  - Ailton R. Oliveira
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.14044
UR  - https://arxiv.org/abs/2609.14044
AB  - We study the Gray-Hervella classes of invariant almost Hermitian structures on the maximal real flag manifold of type π’œ_3. We first obtain an explicit parametrization of all invariant almost Hermitian structures and establish necessary and sufficient conditions for an invariant almost Hermitian structure to belong to each Gray-Hervella class. For each nonempty class, we give an explicit parametrization of the corresponding set of structures, describe it as a smooth manifold and determine its dimension.
ER  -