Quasi generalized CR-null submanifolds
Differential geometry of null submanifolds has numerous applications in mathematical physics, particularly in general relativity (GR) and electromagnetism.
In GR, null submanifolds represent various black hole horizons.
Generalized CR (GCR)-null submanifolds of indefinite almost contact manifolds were introduced by K.
Duggal and B.
Sahin, with the assumption that they are tangent to the structure vector field of the almost contact structure.
Contrary to the above assumption, we have introduced and studied a new class of CR-null submanifold of an indefinite nearly α-Sasakian manifold, called quasi generalized CR (QGCR)-null submanifolds.
We have showed that QGCR-null submanifold include: ascreen QGCR, co-screen QGCR and the well-known GCR-null submanifolds.
We have proved some existence (or non-existence) theorems and provided a thorough study of geometry of their distributions.
Also, we have constructed many examples, where necessary, to illustrate the main ideas.
Samuel Ssekajja hails from Wakiso District, Uganda.
He is currently doing research in mathematics and mathematics Education at the University of KwaZulu-Natal, South Africa.
His research focuses on the differential geometry of submanifolds of semi-Riemannian manifolds, with special attention to null submanifolds and their applications.