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Orthogonal geodesic and minimal distributions. (English) Zbl 0507.53032


MSC:

53C40 Global submanifolds
58A30 Vector distributions (subbundles of the tangent bundles)
53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
53C12 Foliations (differential geometric aspects)
57R30 Foliations in differential topology; geometric theory
53B20 Local Riemannian geometry
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References:

[1] Irl Bivens, Codazzi tensors and reducible submanifolds, Trans. Amer. Math. Soc. 268 (1981), no. 1, 231 – 246. · Zbl 0474.53005
[2] Robert A. Blumenthal, Transversely homogeneous foliations, Ann. Inst. Fourier (Grenoble) 29 (1979), no. 4, vii, 143 – 158 (English, with French summary). · Zbl 0405.57016
[3] Robert A. Blumenthal, Foliated manifolds with flat basic connection, J. Differential Geom. 16 (1981), no. 3, 401 – 406 (1982). · Zbl 0466.57009
[4] Alfred Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715 – 737. · Zbl 0147.21201
[5] H. Huck, R. Roitzsch, U. Simon, W. Vortisch, R. Walden, B. Wegner, and W. Wendland, Beweismethoden der Differentialgeometrie im Grossen, Lecture Notes in Mathematics, Vol. 335, Springer-Verlag, Berlin-New York, 1973 (German). · Zbl 0258.53029
[6] David L. Johnson, Kähler submersions and holomorphic connections, J. Differential Geom. 15 (1980), no. 1, 71 – 79 (1981). · Zbl 0442.53030
[7] David L. Johnson and Lee B. Whitt, Totally geodesic foliations, J. Differential Geom. 15 (1980), no. 2, 225 – 235 (1981). · Zbl 0444.57017
[8] Barrett O’Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459 – 469. · Zbl 0145.18602
[9] Robert C. Reilly, On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space, Comment. Math. Helv. 52 (1977), no. 4, 525 – 533. · Zbl 0382.53038 · doi:10.1007/BF02567385
[10] Bernd Wegner, Codazzi-Tensoren und Kennzeichnungen sphärischer Immersionen, J. Differential Geometry 9 (1974), 61 – 70 (German). · Zbl 0278.53041
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