The First Eigenvalue of P-manifolds

1995/11/24 by Akhil Ranjan, Ranjan, Akhil, G. Santhanam +1
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9511014

17 pages, Latex

arxiv created 1995/11/24 · openalex publication_date 1995/11/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Antonio Ros gave a lower bound for the first eigenvalue λ₁ of Δ of a P-manifold (M, g) in terms of the lower bound on the Ricci curvature Ric_M and asked what happened when this lower bound was achieved. In this paper we look in to this question and show that there are strong implications on the geometry and topology of the underlying manifold. In particular we show that in case of spheres or real projective spaces we have isometry with the standard metric. In other cases, with some additional hypothesis, we again show isometry with standard models.

Citations

• A Generalisation of Obata's theorem

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