SavedAdd your journal

Journals / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 1

The Sampson Laplacian on Negatively Pinched Riemannian Manifolds

Vladimir ROVENSKI
Sergey STEPANOV
Irina TSYGANOK
Pages
91–99
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Some applications of these results to conformal Killing tensors are presented.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We prove vanishing theorems for the kernel of the Sampson Laplacian, acting on symmetric tensors on a Riemannian manifold and estimate its first eigenvalue on negatively pinched Riemannian manifolds.
📊
Key Findings & Data:We prove vanishing theorems for the kernel of the Sampson Laplacian, acting on symmetric tensors on a Riemannian manifold and estimate its first eigenvalue on negatively pinched Riemannian manifolds.
💡
Conclusion & Impact:Some applications of these results to conformal Killing tensors are presented.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Riemannian manifold · Sampson Laplacian · spectral and vanishing theorems

Abstract

We prove vanishing theorems for the kernel of the Sampson Laplacian, acting on symmetric tensors on a Riemannian manifold and estimate its first eigenvalue on negatively pinched Riemannian manifolds. Some applications of these results to conformal Killing tensors are presented.

🔖

Cite This Article

ROVENSKI, V., STEPANOV, S., TSYGANOK, I. (2022). The Sampson Laplacian on Negatively Pinched Riemannian Manifolds. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 1, 91–99. https://ajindex.com/articles/539593

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (21)

  1. Becce A.: Einstein manifolds, Springer-Verlag, Berlin, (1987)
  2. Benn M. and Charlton P.: Dirac symmetry operators from conformal Killing-Yano tensors. Class. Quantum Grav. 14, 1037-1042 (1997)
  3. Berger M. and Ebine D.: Some decomposition of the space of symmetric tensors of a Riemannian manifold. Journal of Differential Geometry. 3,379–392 (1969)
  4. Bochner S. and Yano K.: Curvature and Betti numbers, Princeton Univ. Press, Princeton, (1953)
  5. Bouguignon J.-P.: Formules deWeitzenböck en dimension 4, Geometrie riemannienne en dimension 4. Semin. Arthur Besse, Paris 1978/79, Textes Math., Cedic, Paris. 3, 308–333( 1981)
  6. Burns K. and Katok A.: Manifolds with non-positive curvature. Ergodic Theory of Dynamical Systems. 5:2, 307–317 (1985)
  7. Chow B., Lu P. and Ni L.: Hamilton’s Ricci flow, Providence, AMS, (2006)
  8. Craioveanu M., Puta M. and Rassias T.M.: Old and new aspects in spectral geometry, Kluwer Academic Publishers, London, (2001)
  9. Dairbekov N.S. and Sharafutdinov V.A.: Conformal Killing symmetric tensors on Riemannian manifolds. Mat. Tr. 13:1, 85–145 (2010)
  10. Eastwood M.: Higher symmetries of the Laplacian. Annals of Mathematics. 161, 1645–1665 (2005)
  11. Gibbons G.W. and Perry M.J.:Quantizing gravitational instantons. Nuclear Physics B. 146,I,90–108 (1978)
  12. Gilkey P.R.: Invariant theory, the heat equation, and the Atiyah-Singer index theorem. CRC Press, Washington, (1995)
  13. Goldberg S.I.: Curvature and homology. Dover Publications, New-York, (1998)
  14. Gromov M. and Thurston W.: Pinching constants for hyperbolic manifolds. Invent. Math.89, 1–12 (1987)
  15. Hamenstädt U.: Compact manifolds with 1=4-pinched negative curvature. Lectures Notes in Math., 1481. Global Differential Geometry and Global Analysis, Springer-Verlag, Berlin-Heidelberg, 73–78 (1991)
  16. Heil K., Moroianu A. and Semmelmann U.: Killing and conformal Killing tensors. J. Geom. Phys., 106,383–400 (2016)
  17. Hitchin, N.: A note on vanishing theorems, In: Geometry and Analysis on Manifolds. Progr. Math. 308, 373–382 (2015)
  18. Kashiwada T.: On conformal Killing tensor. Natural. Sci. Rep. Ochanomizu Univ. 19:2, 67–74 (1968)
  19. Kashiwada T.: On the curvature operator of the second kind. Natural Science Report, Ochanomizu University. 44:2, 69-73 (1993)
  20. Lichnerowicz A.: Propagateurs et commutateurs en relativité générate. Publ. Mathématiques de l’IHÉS.10:1, 293–344(1961)
  21. Michel R.: Problème d’analyse géomètrique lié à la con