In this short communication we study supergravity solutions preserving a nonminimal fraction of supersymmetries by determining the existence of additional non-space-like isometries in the class of higher-dimensional Kundt space-time admitting a covariantly constant

null vector field (CCNV) [6, 7].

It follows that dim [P.sub.2] [less than or equal to] dim [P.sup.[omega].sub.1] = 1, so the curve [[??].sub.2] is a straight line, which may be parametrized as follows: [[??].sub.2]([upsilon]) = [e.sub.0][upsilon], where [e.sub.0] is a

null vector of [D.sup.2].

Therefore, the complex vector P is a complex

null vector which represents the lightlike nature of the photon.

The set of all integral curves given by a unit nonnull or

null vector field u is called the congruence of nonnull or null curves.

Nulling: where we use the

null vector wki to null out the undesired signals and obtain the required one.

Since A(x - y) must be in R(A) and p is not, both sides vanish, implying that x - y is a

null vector of A and q* y must be zero.

If g(D(s),D(s)) = 0 for all s [member of] [0, L], then u(s) = 0 and the direction D(s) is a

null vector given by

(iii) timelike vector is never orthogonal to a

null vector.

A regular curve [alpha] : I [right arrow] [R.sup.3.sub.1], I [subset] R in [R.sup.3.sub.1] is said to be spacelike, timelike and null curve if the velocity vector [alpha][phi](t) is a spacelike, timelike and

null vector, respectively [3].

(PN1) [v.sub.p] = [[epsilon].sub.0] iff (if and only if) p = [theta], here [theta] is the

null vector of V;

Then [[xi].sub.3] is the vector field [C.sup.[perpendicular]] and [[xi].sub.4] is the unique

null vector field perpendicular to the plane {[[xi].sub.1], [[xi].sub.2]}, such that {[[xi].sub.3], [[xi].sub.4]) = 1.

where [lambda] is a complex constant and y is a constant vector (an element of the space [C.sup.N]) which depends upon [lambda] and which we desire to be nontrivial, that is, not equal to 0, the

null vector. Substituting (1.10) into (1.8), we obtain