Some differential operators in the symmetric bundle

• Autorzy: Kimaczyńska A.

Identyfikatory

DOI

10.17512/jamcm.2017

• Języki publikacji: EN

Abstrakty

EN

Some natural differential operators in the bundles of symmetric tensors and symmetric tensors with values in the tangent bundle are investigated. Applications in geometry, physics and tomography are also reviewed.

Słowa kluczowe

EN

symmetric tensors; symmetric derivative; gradient; divergence; Weitzenböck type formula

PL

operator różnicowy; tensory symetryczne; pochodna symetryczna; gradient

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2017
• Tom: Vol. 16, nr 3
• Strony: 27--36
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Kimaczyńska A.

• Institute of Mathematics and Computer Science, University of Lodz Lodz, Poland

Bibliografia

• [1] Balcerzak B., Pierzchalski A., Generalized gradients on Lie algebroids, Ann. Global Anal. Geom. 2013, 44(3), 319-337.
• [2] Stepanov S.E., Mikĕs J., The spectral theory of the Yano rough Laplacian with some of its applications, Ann Global Anal. Geom. 2015, 48, 37-46.
• [3] Heil K., Moroianu A., Semmelmann U., Killing and conformal Killing tensors, J. Geom. Phys. 2016, 106, 383-400.
• [4] Reimann H.M., A rotation invariant differential equation for vector fields, Ann. Scuola Norm. Sup. Pisa 1982, 9, 160-174.
• [5] Kimaczyńska A., The differential operators in the bundle of symmetric tensors on a Riemannian manifold, PhD thesis, Łódź University, Faculty of Mathematics and Computer Science, Łódź 2016, 64 p.
• [6] Kimaczyńska A., Pierzchalski A., Elliptic operators in the bundle of symmetric tensors, Banach Center Publications (To appear).
• [7] Sampson J.H., On a theorem of Chern, AMS 1973, 177, 141-153.
• [8] Kobayashi S., Nomizu K., Foundations of differential geometry II, Interscience Publishers, New York - London 1969.
• [9] Yu Y., The Index Theorem and the Heat Equation Method, World Scientific, Singapore – New Jersey - London - Hong Kong 2000.
• [10] Kozłowski W., Pierzchalski A., Natural boundary value problems for weighted form Laplacians, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 2008, (5), VII, 343-367.
• [11] Pierzchalski A., Ricci curvature and quasiconformal deformations of a Riemannian manifold, Manuscripta Mathematica 1989, 66, 113-127.
• [12] Dairbekov N.S., Sharafutdinov V.A., Conformal Killing symmetric tensor fields on Riemannian manifolds (Russian), Mat. Tr. 2010, 13, no. 1, 85-145; translation in Siberian Adv. Math. 2011, 21, 1, 1-41.
• [13] Stepanov S., Tsyganok I., Aleksandrova I., A remark on Laplacian operator which acts on symmetric tensors, arXiv:1411.1928.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).