Geodesic
Submanifolds of an even-dimensional manifold structured by a~$\mathcal T$-parallel connection
Lobachevskii journal of mathematics, Tome 13 (2003), pp. 81-85

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Even-dimensional manifolds $N$ structured by a $\mathcal T$-parallel connection have been defined and studied in [DR], [MRV]. In the present paper, we assume that $N$ carries a $(1,1)$-tensor field $J$ of square ${-1}$ and we consider an immersion $x : M\to N$. It is proved that any such $M$ is a CR-product [B] and one may decompose $M$ as $M=M_D\times M_{D^\perp}$, where $M_D$ is an invariant submanifold of $M$ and $M_{D\perp}$ is an antiinvariant submanifold of $M$. Some other properties regarding the immersion $x:M\to N$ are discussed. 
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     author = {K. Matsumoto and A. Mihai and D. Naitza},
     title = {Submanifolds of an even-dimensional manifold structured by a~$\mathcal T$-parallel connection},
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     pages = {81--85},
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     url = {http://geodesic.mathdoc.fr/item/LJM_2003_13_a8/}
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K. Matsumoto; A. Mihai; D. Naitza. Submanifolds of an even-dimensional manifold structured by a~$\mathcal T$-parallel connection. Lobachevskii journal of mathematics, Tome 13 (2003), pp. 81-85. http://geodesic.mathdoc.fr/item/LJM_2003_13_a8/