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<p>We study general rotational surfaces in the pseudo-Euclidean 4-dimensional space with neutral metric and describe the behavior of geometric objects, such as Killing vector fields (and in particular homothetic vector fields), divergence-free vector fields, co-closed and harmonic one-forms, and also harmonic functions. We classify geodesic and parallel vector fields, geodesic curves, concircular vector fields and concircular functions, and also concurrent vector fields and functions whose gradient is concurrent. Our results are new, as they have not been obtained in the Euclidean and Minkowski framework. The tools here are taken from both differential geometry and partial and ordinary differential equations.</p>

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Special Structures on General Rotational Surfaces in the Pseudo-Euclidean 4-space with Neutral Metric

  • 期刊论文

  • 发表日期：

    2026年4月24日

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  • Cornelia-Livia Bejan,
  • Velichka Milousheva

摘要

We study general rotational surfaces in the pseudo-Euclidean 4-dimensional space with neutral metric and describe the behavior of geometric objects, such as Killing vector fields (and in particular homothetic vector fields), divergence-free vector fields, co-closed and harmonic one-forms, and also harmonic functions. We classify geodesic and parallel vector fields, geodesic curves, concircular vector fields and concircular functions, and also concurrent vector fields and functions whose gradient is concurrent. Our results are new, as they have not been obtained in the Euclidean and Minkowski framework. The tools here are taken from both differential geometry and partial and ordinary differential equations.