메뉴 건너뛰기




Volumn 91, Issue 1, 2002, Pages 175-196

Collapsing and Dirac-type operators

Author keywords

Collapsing; Dirac operator; Eigenvalues

Indexed keywords


EID: 0141788272     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1016247531019     Document Type: Article
Times cited : (27)

References (22)
  • 1
    • 0009139895 scopus 로고    scopus 로고
    • The Dirac operator on nilmanifolds and collapsing circle bundles
    • Ammann B. and Bar, C.: The Dirac operator on nilmanifolds and collapsing circle bundles, Ann. Global Anal. Geom. 16 (1998), 221-253.
    • (1998) Ann. Global Anal. Geom. , vol.16 , pp. 221-253
    • Ammann, B.1    Bar, C.2
  • 3
    • 0039087272 scopus 로고
    • Characteristic classes of compact solvmanifolds
    • Auslander L. and Szczarba, R.: Characteristic classes of compact solvmanifolds, Ann. of Math. 76 (1962), 1-8.
    • (1962) Ann. of Math. , vol.76 , pp. 1-8
    • Auslander, L.1    Szczarba, R.2
  • 6
    • 84968484140 scopus 로고
    • From vanishing theorems to estimating theorems: The Bochner technique revisited
    • Berard, P.: From vanishing theorems to estimating theorems: the Bochner technique revisited, Bull. Amer. Math. Soc. 19 (1988), 371-406.
    • (1988) Bull. Amer. Math. Soc. , vol.19 , pp. 371-406
    • Berard, P.1
  • 9
    • 84967772588 scopus 로고
    • Flat vector bundles, direct images and higher real analytic torsion
    • Bismut J.-M. and Lott, J.: Flat vector bundles, direct images and higher real analytic torsion, J. Amer. Math. Soc. 8 (1995), 291-363.
    • (1995) J. Amer. Math. Soc. , vol.8 , pp. 291-363
    • Bismut, J.-M.1    Lott, J.2
  • 10
    • 0001623209 scopus 로고
    • Spineurs, opérateurs de Dirac et variations de métriques
    • Bourguignon J.-P. and Gauduchon, P.: Spineurs, opérateurs de Dirac et variations de métriques, Comm. Math. Phys. 144 (1992), 581-599.
    • (1992) Comm. Math. Phys. , vol.144 , pp. 581-599
    • Bourguignon, J.-P.1    Gauduchon, P.2
  • 11
    • 84968509403 scopus 로고
    • Nilpotent structures and invariant metrics on collapsed manifolds
    • Cheeger, J. Fukaya K. and Gromov, M.: Nilpotent structures and invariant metrics on collapsed manifolds, J. Amer. Math. Soc. 5 (1992), 327-372.
    • (1992) J. Amer. Math. Soc. , vol.5 , pp. 327-372
    • Cheeger, J.1    Fukaya, K.2    Gromov, M.3
  • 12
    • 84968510067 scopus 로고
    • Adiabatic limits, nonmultiplicativity of signature, and Leray spectral sequence
    • Dai, X.: Adiabatic limits, nonmultiplicativity of signature, and Leray spectral sequence, J. Amer. Math. Soc. 4 (1991), 265-321.
    • (1991) J. Amer. Math. Soc. , vol.4 , pp. 265-321
    • Dai, X.1
  • 13
    • 84972567499 scopus 로고
    • Pure points spectrum and negative curvature for noncompact manifolds
    • Donnelly H. and Li, P.: Pure points spectrum and negative curvature for noncompact manifolds, Duke Math. J. 46 (1979), 497-503.
    • (1979) Duke Math. J. , vol.46 , pp. 497-503
    • Donnelly, H.1    Li, P.2
  • 14
    • 0040460272 scopus 로고
    • Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
    • Fukaya, K.: Collapsing of Riemannian manifolds and eigenvalues of Laplace operator, Invent Math. 87 (1987), 517-547.
    • (1987) Invent Math. , vol.87 , pp. 517-547
    • Fukaya, K.1
  • 15
    • 84972535799 scopus 로고
    • A boundary for the set of the Riemannian manifolds with bounded curvatures and diameters
    • Fukaya, K.: A boundary for the set of the Riemannian manifolds with bounded curvatures and diameters, J. Differential Geom. 28 (1988), 1-21.
    • (1988) J. Differential Geom. , vol.28 , pp. 1-21
    • Fukaya, K.1
  • 16
    • 84972579144 scopus 로고
    • Collapsing Riemannian manifolds to ones with lower dimension II
    • Fukaya, K.: Collapsing Riemannian manifolds to ones with lower dimension II, J. Math. Soc. Japan 41 (1989), 333-356.
    • (1989) J. Math. Soc. Japan , vol.41 , pp. 333-356
    • Fukaya, K.1
  • 17
    • 0037104046 scopus 로고    scopus 로고
    • Collapsing and the differential form Laplacian: The case of a smooth limit space
    • to appear
    • Lott, J.: Collapsing and the differential form Laplacian: the case of a smooth limit space, to appear in Duke Math J., http://www.math.lsa.umich.edu/~lott.
    • Duke Math J.
    • Lott, J.1
  • 18
    • 0141570803 scopus 로고    scopus 로고
    • A-Genus and collapsing
    • Lott, J.: A-Genus and collapsing, J. of Geom. Anal. 10 (2000), 529-543.
    • (2000) J. of Geom. Anal. , vol.10 , pp. 529-543
    • Lott, J.1
  • 19
    • 0035315395 scopus 로고    scopus 로고
    • On the spectrum of a finite-volume negatively-curved manifold
    • Lott, J.: On the spectrum of a finite-volume negatively-curved manifold, Amer. J. Math. 123 (2001), 185-205.
    • (2001) Amer. J. Math. , vol.123 , pp. 185-205
    • Lott, J.1
  • 21
    • 0030547161 scopus 로고    scopus 로고
    • On the fundamental groups of manifolds of positive sectional curvature
    • Rong, X.: On the fundamental groups of manifolds of positive sectional curvature, Ann. of Math. 143 (1996), 397-411.
    • (1996) Ann. of Math. , vol.143 , pp. 397-411
    • Rong, X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.