On integral cohomology algebra of some oriented Grassmann manifolds

The integral cohomology algebra of ${\tilde{G}}_{6,3}$ has been determined in the recent work of Kalafat and Yalçınkaya. We completely determine the integral cohomology algebra of ${\tilde{G}}_{n,3}$ for $n=8$ and $n=10$. The main method used to describe these algebras is the Leray–Serre spectral sequence. We also illustrate this method by determining the integral cohomology algebra of ${\tilde{G}}_{n,2}$ for $n$ odd.