Abstract
In this paper, totally geodesic affine immersionsf: (M, ∇) →\((\bar M,\bar \nabla )\) are studied in the case when\((\bar M,\bar \nabla )\) is an affine manifold of recurrent curvature. It is proved that(M, ∇) if flat or of recurrent curvature. And iff is additionally umbilical with the shape tensorA ≠ 0 and dimM ≥3, then(M, ∇) is locally projectively flat. Examples of such immersions are also stated.
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Olszak, Z. On totally geodesic affine immersions. J Geom 47, 115–124 (1993). https://doi.org/10.1007/BF01223810
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DOI: https://doi.org/10.1007/BF01223810