Answer: Texas A & M recommends the following groundcovers for sunny slopes:
Asiatic jasmine (Trachelospermum asiaticum) with evergreen deep green or variegated foliage. Confederate jasmine (Trachelospermum jasminoides), an evergreen with fragrant, white spring flowers. English ivy (Hedera helix), an evergreen; green or variegated foliage. Liriope (Liriope muscari), an evergreen, grass-like foliage; purple blooms; varieties: big blue, gigantic. Monkey grass (Ophiopogon japonicus), an evergreen, grass-like foliage; dwarf and standard varieties. Prostrate rosemary (Rosmarinus officinalis) with Grayish-green, fragrant foliage; light blue flowers.
Santolina (Santolina sp.) Species with green or silver foliage. Vinca (Vinca major) a trailing plant with blue flowers and dark green foliage.
Hope one of these works in your landscape.
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