What is the 'well-known' circle bundle $p:V_{2}(\mathbb{R}^{6})\rightarrow G_{2}(\mathbb{C}^{4})$? Here $V_{2}(\mathbb{R}^{6})$ denotes the real Stiefel manifold of orthonormal 2 frames and $G_{2}(\mathbb{C}^{4})$ is the complex Grassmannian of two planes.
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You probably need to add some context. Are you reading a paper? A textbook? Some notes? What is the text about? Can you give the entire paragraph? – Danu Aug 23 '17 at 21:46
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I'm guessing this paper https://arxiv.org/pdf/1209.1587.pdf – Tyrone Aug 24 '17 at 15:50