Geodesic
Characteristic directions of a~point mapping of $P_m$ into~$P_n$
Itogi Nauki i Tekhniki. Seriya Problemy Geometrii. Trudy Geometricheskogo Seminara, Trudy Geometricheskogo Seminara, Tome 3 (1971), pp. 235-242

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The notion of characteristic directions, well known for the case of point correspondences between projective spaces of the same dimension $n$ is generalized to the case of mappings $P_m$ into $P_n$, when $m\ne n$. If $m$ the special importance of the asymptotic directions of the image surface $V_m\subset Р_n$ is shown. These and only these directions can be regarded as characteristic ones for some mappings $P_m$ into $P_n$, having the image $V_m$. If $m>n$ some preliminary facts concerning the characteristic directions are regarded and the case $P_3\to P_2$ is discussed. 
@article{INTG_1971_3_a10,
     author = {V. V. Ryzhkov},
     title = {Characteristic directions of a~point mapping of $P_m$ into~$P_n$},
     journal = {Itogi Nauki i Tekhniki. Seriya Problemy Geometrii. Trudy Geometricheskogo Seminara},
     pages = {235--242},
     publisher = {mathdoc},
     volume = {3},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTG_1971_3_a10/}
}
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V. V. Ryzhkov. Characteristic directions of a~point mapping of $P_m$ into~$P_n$. Itogi Nauki i Tekhniki. Seriya Problemy Geometrii. Trudy Geometricheskogo Seminara, Trudy Geometricheskogo Seminara, Tome 3 (1971), pp. 235-242. http://geodesic.mathdoc.fr/item/INTG_1971_3_a10/