Abstract:
We give a comparative analysis of the spectral
properties of the Hodge–de Rham and Tachibana
operators on compact Riemannian manifolds whose
curvature operator is bounded and has a definite sign.
We find bounds for their spectra and estimate
their multiplicities.
Citation:
S. E. Stepanov, J. Mikeš, “The Hodge–de Rham Laplacian and Tachibana operator on a compact Riemannian
manifold with curvature operator of definite sign”, Izv. Math., 79:2 (2015), 375–387
\Bibitem{SteMik15}
\by S.~E.~Stepanov, J.~Mike{\v s}
\paper The Hodge--de Rham Laplacian and Tachibana operator on a~compact Riemannian
manifold with curvature operator of definite sign
\jour Izv. Math.
\yr 2015
\vol 79
\issue 2
\pages 375--387
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Linking options:
https://www.mathnet.ru/eng/im8156
https://doi.org/10.1070/IM2015v079n02ABEH002746
https://www.mathnet.ru/eng/im/v79/i2/p167
This publication is cited in the following 8 articles:
Josef Mikeš, Sergey Stepanov, Irina Tsyganok, “New applications of the Ahlfors Laplacian: Ricci almost solitons and general relativistic vacuum constraint equations”, Journal of Geometry and Physics, 2024, 105414
Zhang J., Zhang T., “Focusing Algorithm of Automatic Control Microscope Based on Digital Image Processing”, J. Sens., 2021 (2021), 5643054
I. G. Shandra, S. E. Stepanov, J. Mikes, “On higher-order codazzi tensors on complete Riemannian manifolds”, Ann. Glob. Anal. Geom., 56:3 (2019), 429–442
Josef Mikeš et al., Differential Geometry of Special Mappings, 2019
Josef Mikeš et al., Differential Geometry of Special Mappings, 2019
S. Stepanov, I. Tsyganok, “Conformal Killing $L^2$-forms on complete Riemannian manifolds with nonpositive curvature operator”, J. Math. Anal. Appl., 458:1 (2018), 1–8
S. E. Stepanov, I. I. Tsyganok, T. V. Dmitrieva, “Harmonic and conformally Killing forms on complete Riemannian manifold”, Russian Math. (Iz. VUZ), 61:3 (2017), 44–48
Mikes J., Stepanova E., Vanzurova A., “Differential Geometry of Special Mappings”, Differential Geometry of Special Mappings, Palacky Univ, 2015, 1–566
Citation in format AMSBIB
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