Geodesic
Manifolds of the homotopy type of the product of two projective spaces
Sbornik. Mathematics, Tome 25 (1975) no. 4, pp. 471-486 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper the sets of homotopy triangulations of the manifold $RP^k\times RP^l$ are computed for all $k,l\geqslant3$ except for the case when $k$ and $l$ are even and $k+l=4r$. Bibliography: 11 titles. 
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A. F. Kharshiladze. Manifolds of the homotopy type of the product of two projective spaces. Sbornik. Mathematics, Tome 25 (1975) no. 4, pp. 471-486. http://geodesic.mathdoc.fr/item/SM_1975_25_4_a0/

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[11] S. P. Novikov, “Ermitovy analogi $K$-teorii. I, II”, Izv. AN SSSR, seriya matem., 34 (1970), 253–288 ; 475–500 | Zbl | Zbl