Geodesic
Characterization of totally geodesic foliations with integrable and parallelizable normal bundle
Glasgow mathematical journal, Tome 65 (2023) no. 1, pp. 128-137

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DOI

In this work, we study foliations of arbitrary codimension $\mathfrak{F}$ with integrable normal bundles on complete Riemannian manifolds. We obtain a necessary and sufficient condition for $\mathfrak{F}$ to be totally geodesic. For this, we introduce a special number $\mathfrak{G}_{\mathfrak{F}}^{\alpha}$ that measures when the foliation ceases to be totally geodesic. Furthermore, applying some maximum principle we deduce geometric properties for $\mathfrak{F}$. We conclude with a geometrical version of Novikov’s theorem (Trans. Moscow Math. Soc. (1965), 268–304), for Riemannian compact manifolds of arbitrary dimension.
DOI : 10.1017/S0017089522000179
Mots-clés : Complete Riemannian manifold, Orthogonal foliations, Totally geodesic and umbilical 
Silva, Euripedes C. da; Souza, David C.; Reis, Fernando P.P. Characterization of totally geodesic foliations with integrable and parallelizable normal bundle. Glasgow mathematical journal, Tome 65 (2023) no. 1, pp. 128-137. doi: 10.1017/S0017089522000179
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     title = {Characterization of totally geodesic foliations with integrable and parallelizable normal bundle},
     journal = {Glasgow mathematical journal},
     pages = {128--137},
     year = {2023},
     volume = {65},
     number = {1},
     doi = {10.1017/S0017089522000179},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089522000179/}
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