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Volumn 40, Issue 2, 1996, Pages 194-201

Riemannian submersions which preserve the eigenforms of the Laplacian

(2)  Gilkey, P B a   Park, J H a  

a NONE

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EID: 0000365880     PISSN: 00192082     EISSN: None     Source Type: Journal    
DOI: 10.1215/ijm/1255986099     Document Type: Article
Times cited : (10)

References (11)
  • 1
    • 84972545964 scopus 로고
    • Laplacians and Riemannian submersions with totally geodesic fibers
    • L. Berard Bergery and J. P. Bourguignon, Laplacians and Riemannian submersions with totally geodesic fibers, Illinois J. Math. 26 (1982), 181-200.
    • (1982) Illinois J. Math. , vol.26 , pp. 181-200
    • Berard Bergery, L.1    Bourguignon, J.P.2
  • 2
    • 84972529830 scopus 로고
    • On the group of diffeomorphism commuting with an elliptic operator
    • K. Furutani, On the group of diffeomorphism commuting with an elliptic operator, J. Math. Soc. Japan 35 (1983), 153-162; see also On a differentiable map commuting with an elliptic pseudo-differential operator, J. Math Kyoto Univ. 24 (1984), 197-203.
    • (1983) J. Math. Soc. Japan , vol.35 , pp. 153-162
    • Furutani, K.1
  • 3
    • 84972529830 scopus 로고
    • On a differentiable map commuting with an elliptic pseudo-differential operator
    • K. Furutani, On the group of diffeomorphism commuting with an elliptic operator, J. Math. Soc. Japan 35 (1983), 153-162; see also On a differentiable map commuting with an elliptic pseudo-differential operator, J. Math Kyoto Univ. 24 (1984), 197-203.
    • (1984) J. Math Kyoto Univ. , vol.24 , pp. 197-203
  • 5
    • 0039807434 scopus 로고
    • Eigenvalues of the Laplacian and Riemannian submersions
    • P. Gilkey and J. H. Park, Eigenvalues of the Laplacian and Riemannian submersions, Yokohama Math. J. 43 (1995), 7-11.
    • (1995) Yokohama Math. J. , vol.43 , pp. 7-11
    • Gilkey, P.1    Park, J.H.2
  • 6
    • 84972545680 scopus 로고
    • Riemannian submersions commuting with the Laplacian
    • S. I. Goldberg and T. Ishihara, Riemannian submersions commuting with the Laplacian, J. Differential Geom. 13 (1978), 139-144.
    • (1978) J. Differential Geom. , vol.13 , pp. 139-144
    • Goldberg, S.I.1    Ishihara, T.2
  • 7
    • 0000430059 scopus 로고
    • A mapping of Riemannian manifolds which preserves harmonic functions
    • T. Ishihara, A mapping of Riemannian manifolds which preserves harmonic functions, J. Math. Kyoto Univ. 19 (1979), 215-229.
    • (1979) J. Math. Kyoto Univ. , vol.19 , pp. 215-229
    • Ishihara, T.1
  • 8
    • 0002179237 scopus 로고
    • Some eigenforms of the Laplace-Beltrami operators in a Kiemannian submersion
    • Y. Muto, Some eigenforms of the Laplace-Beltrami operators in a Kiemannian submersion, J. Korean Math. Soc. 15 (1978), 39-57.
    • (1978) J. Korean Math. Soc. , vol.15 , pp. 39-57
    • Muto, Y.1
  • 9
    • 84972514588 scopus 로고
    • Riemannian submersion and the Laplace-Beltrami operator
    • _, Riemannian submersion and the Laplace-Beltrami operator, Kodai Math. J. 1 (1978), 329-338.
    • (1978) Kodai Math. J. , vol.1 , pp. 329-338
  • 10
    • 0002439907 scopus 로고
    • Manifold maps commuting with the Laplacian
    • B. Watson, Manifold maps commuting with the Laplacian, J. Differential Geom. 8 (1973), 85-94.
    • (1973) J. Differential Geom. , vol.8 , pp. 85-94
    • Watson, B.1
  • 11
    • 84972559671 scopus 로고
    • δ commuting mappings and Betti numbers
    • _, δ commuting mappings and Betti numbers, Tohoku Math. J. 27 (1975), 135-152.
    • (1975) Tohoku Math. J. , vol.27 , pp. 135-152


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.